Edit Profile (opens in new tab) Fairweather, Graeme Co-Author Distance Author ID: fairweather.graeme Published as: Fairweather, Graeme; Fairweather, G. Documents Indexed: 120 Publications since 1964, including 3 Books 3 Contributions as Editor Co-Authors: 78 Co-Authors with 111 Joint Publications 1,805 Co-Co-Authors all top 5 Co-Authors 12 single-authored 21 Bialecki, Bernard 19 Karageorghis, Andreas 9 Keast, Patrick 8 Pani, Amiya Kumar 7 Mitchell, Andrew Ronald 6 Fernandes, Ryan I. 5 Diaz, Julio Cesar 5 López-Marcos, Juan Carlos 4 Gladwell, Ian 4 Johnston, Roy L. 4 Nguyen, Que N. 4 Sun, Weiwei 3 Bennett, Karin R. 3 Dendy, Joel E. jun. 3 Gourlay, A. R. 3 Johnson, J. Peter 3 Li, Bingkun 3 Robinson, Mark P. 3 Shippy, David J. 3 Yang, Xuehua 3 Zhang, Haixiang 2 Bhal, Santosh Kumar 2 Danumjaya, Palla 2 Du, Kui 2 Khebchareon, Morrakot 2 Kondapalli, Prasanna S. 2 Majaess, Fouad 2 Martin, Paul Andrew 2 Micula, Gheorghe 2 Saylor, Annie V. 2 Seward, Wendy L. 2 Smyrlis, Yiorgos-Sokratis 2 Tankelevich, Roman 2 Xu, Da 2 Yanik, Elizabeth Greenwell 1 Amodio, Pierluigi 1 Cai, Xiao-Chuan 1 Cash, Jeff R. 1 Christie, Ian 1 Dryja, Maksymilian 1 Dupont, Todd F. 1 Greenwell-Yanik, C. E. 1 Karageorhis, A. 1 Kasibhatla, Prasad S. 1 Knudson, David B. 1 Kraut, G. L. 1 Leimkuhler, Benedict J. 1 Li, Zhi 1 Lin, Qun 1 Lin, Yanping 1 Lipman, D. Abram 1 Lou, Zhou-Ming 1 Ma, Heping 1 Maack, Jon 1 Maack, Jonathan 1 Maede, Daniel 1 Mishra, Pankaj Kumar 1 Muir, Paul H. 1 Navon, Ionel Michael 1 Paprzycki, Marcin 1 Pew, Jack 1 Qiu, Wenlin 1 Remington, Karin A. 1 Rizzo, Frank Joseph 1 Rudolphi, Thomas J. 1 Sanz-Serna, Jesús María 1 Saylor, Rick D. 1 Sloan, Ian Hugh 1 Tannahill, Connor 1 Tripathi, Lok Pati 1 Van Vleck, Erik S. 1 Vedha-Nayagam, M. 1 Wang, Junping 1 Weinberg, Gadalia M. 1 Wright, R. W. 1 Wu, Yensen S. 1 Yan, Yi 1 Zhang, Shuhua all top 5 Serials 16 SIAM Journal on Numerical Analysis 7 IMA Journal of Numerical Analysis 7 Journal of Computational Physics 6 Mathematics of Computation 5 ACM Transactions on Mathematical Software 5 Numerische Mathematik 4 Journal of Computational and Applied Mathematics 4 Numerical Methods for Partial Differential Equations 4 Numerical Algorithms 3 International Journal for Numerical Methods in Engineering 3 Applied Numerical Mathematics 3 Journal of Scientific Computing 3 SIAM Journal on Scientific Computing 3 Advances in Computational Mathematics 3 Engineering Analysis with Boundary Elements 2 Computers & Mathematics with Applications 2 Journal of the Institute of Mathematics and its Applications 2 BIT 2 The Computer Journal. Section A / Section B 2 SIAM Review 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Calcolo 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Scientific and Statistical Computing 1 Numerical Heat Transfer 1 Communications in Applied Numerical Methods 1 Computational Mechanics 1 Mathematical and Computer Modelling 1 Applied Mathematical Modelling 1 Studia Universitatis Babeș-Bolyai. Mathematica 1 Revue d’Analyse Numérique et de Théorie de l’Approximation 1 Numerical Linear Algebra with Applications 1 East-West Journal of Numerical Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Journal of Computational Acoustics 1 Journal of the Society for Industrial & Applied Mathematics 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Lecture Notes in Pure and Applied Mathematics 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 Advances in Applied Mathematics and Mechanics 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 103 Numerical analysis (65-XX) 54 Partial differential equations (35-XX) 16 Integral equations (45-XX) 11 Ordinary differential equations (34-XX) 11 Fluid mechanics (76-XX) 8 Mechanics of deformable solids (74-XX) 6 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 3 General and overarching topics; collections (00-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 98 Publications have been cited 2,297 times in 1,430 Documents Cited by ▼ Year ▼ The method of fundamental solutions for elliptic boundary value problems. Zbl 0922.65074Fairweather, Graeme; Karageorghis, Andreas 487 1998 The method of fundamental solutions for scattering and radiation problems. Zbl 1060.76649Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A. 122 2003 The method of fundamental solutions for the numerical solution of the biharmonic equation. Zbl 0618.65108Karageorghis, Andreas; Fairweather, Graeme 107 1987 Finite element methods for parabolic and hyperbolic partial integro- differential equations. Zbl 0657.65142Yanik, Elizabeth G.; Fairweather, Graeme 90 1988 Finite element Galerkin methods for differential equations. Zbl 0372.65044Fairweather, Graeme 64 1978 FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. Zbl 0516.65013Diaz, J. C.; Fairweather, G.; Keast, P. 61 1983 Orthogonal spline collocation methods for partial differential equations. Zbl 0971.65105Bialecki, B.; Fairweather, G. 61 2001 \(H^1\)-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101Pani, Amiya K.; Fairweather, Graeme 53 2002 Orthogonal spline collocation methods for some partial integrodifferential equations. Zbl 0756.65157Yan, Yi; Fairweather, Graeme 47 1992 The method of fundamental solutions for problems in potential flow. Zbl 0546.76021Johnston, R. L.; Fairweather, G. 44 1984 A new computational procedure for A.D.I. methods. Zbl 0252.65072Fairweather, G.; Mitchell, A. R. 44 1967 Three-level Galerkin methods for parabolic equations. Zbl 0313.65107Dupont, Todd; Fairweather, Graeme; Johnson, J. Peter 36 1974 The method of fundamental solutions for axisymmetric potential problems. Zbl 0932.74078Karageorghis, Andreas; Fairweather, Graeme 34 1999 ADI orthogonal spline collocation methods for parabolic partial integro-differential equations. Zbl 1191.65186Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 34 2010 Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. Zbl 0806.65123Robinson, Mark P.; Fairweather, Graeme 33 1994 An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation. Zbl 1328.65216Fairweather, Graeme; Yang, Xuehua; Xu, Da; Zhang, Haixiang 33 2015 Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term. Zbl 1160.65068Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 33 2008 The method of fundamental solutions for axisymmetric elasticity problems. Zbl 1011.74005Karageorghis, A.; Fairweather, G. 32 2000 The reformulation and numerical solution of certain nonclassical initial- boundary value problems. Zbl 0722.65062Fairweather, Graeme; Saylor, Rick D. 32 1991 Spline collocation methods for a class of hyperbolic partial integro- differential equations. Zbl 0814.65137Fairweather, Graeme 30 1994 Matrix decomposition algorithms for elliptic boundary value problems: A survey. Zbl 1208.65036Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 30 2011 Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0595.65122Greenwell-Yanik, C. E.; Fairweather, G. 29 1986 Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Zbl 0868.65068Fairweather, G.; López-Marcos, J. C. 29 1996 Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0768.65067Fernandes, Ryan I.; Fairweather, Graeme 28 1993 Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. Zbl 0911.65095Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 26 1998 Algorithms for almost block diagonal linear systems. Zbl 1062.65031Fairweather, Graeme; Gladwell, Ian 25 2004 Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations. Zbl 0123.12001Mitchell, A. R.; Fairweather, G. 24 1964 The simple layer potential method of fundamental solutions for certain biharmonic problems. Zbl 0687.76028Karageorghis, Andreas; Fairweather, Graeme 23 1989 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems. Zbl 1284.65026Fernandes, Ryan I.; Fairweather, Graeme 22 2012 Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. Zbl 0752.65076Bialecki, Bernard; Fairweather, Graeme; Bennett, Karin R. 22 1992 The Almansi method of fundamental solutions for solving biharmonic problems. Zbl 0639.65066Karageorghis, Andreas; Fairweather, Graeme 22 1988 The method of fundamental solutions for the solution of nonlinear plane potential problems. Zbl 0676.65110Karageorghis, A.; Fairweather, G. 22 1989 A high accuracy alternating direction method for the wave equation. Zbl 0221.65180Fairweather, G.; Mitchell, A. R. 21 1965 Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Zbl 0781.65031Bialecki, Bernard; Fairweather, Graeme 19 1993 An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. Zbl 0747.65082Fernandes, Ryan I.; Fairweather, Graeme 19 1991 Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0295.65062Dendy, J. E. jun.; Fairweather, G. 18 1975 Some stable difference approximations to a fourth-order parabolic partial differential equation. Zbl 0147.13801Fairweather, G.; Gourlay, A. R. 18 1967 Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. Zbl 1051.65018Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M. 17 2000 Compact optimal quadratic spline collocation methods for the Helmholtz equation. Zbl 1218.65135Fairweather, Graeme; Karageorghis, Andreas; Maack, Jon 16 2011 On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. Zbl 0397.65080Fairweather, Graeme; Rizzo, Frank J.; Shippy, David J.; Wu, Yensen S. 15 1979 A backward Euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation. Zbl 1352.65392Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da 15 2015 A box method for a nonlinear equation of population dynamics. Zbl 0734.92023Fairweather, G.; López-Marcos, J. C. 15 1991 The method of fundamental solutions for transmission and scattering of elastic waves. Zbl 0825.73150Kondapalli, Prasanna S.; Shippy, Davdi J.; Fairweather, Graeme 14 1992 Potential field based geometric modelling using the method of fundamental solutions. Zbl 1130.65035Tankelevich, Roman; Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 14 2006 Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods. Zbl 1388.76359Fairweather, Graeme; Lin, Qun; Lin, Yanping; Wang, Junping; Zhang, Shuhua 14 2006 Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems. Zbl 0820.65009Bialecki, Bernard; Fairweather, Graeme 12 1995 Some high accuracy difference with a Splitting operator for equations of parabolic and elliptic type. Zbl 0148.39403Fairweather, G.; Gourlay, A. R.; Mitchell, A. R. 12 1967 The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65050Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 11 1992 Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65051Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 11 1992 Matrix decomposition algorithms for modified spline collocation for Helmholtz problems. Zbl 1035.65135Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 11 2003 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. Zbl 1352.65393Fernandes, Ryan I.; Bialecki, Bernard; Fairweather, Graeme 11 2015 Orthogonal spline collocation methods for biharmonic problems. Zbl 0908.65103Lou, Zhou-Ming; Bialecki, Bernard; Fairweather, Graeme 10 1998 A note on the efficient implementation of certain Padé methods for linear parabolic problems. Zbl 0384.65036Fairweather, Graeme 10 1978 An H\(^{1}\)-Galerkin mixed finite element method for an evolution equation with a positive-type memory term. Zbl 1047.65085Pani, Amiya K.; Fairweather, Graeme 10 2002 Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations. Zbl 1168.76037Fairweather, Graeme; Ma, Heping; Sun, Weiwei 10 2008 On the eigenvalues and eigenvectors of a class of Hessenberg matrices. Zbl 0217.52603Fairweather, G. 10 1971 Discrete-time orthogonal spline collocation methods for vibration problems. Zbl 1028.74022Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 9 2002 A fourth-order cubic spline method for linear second-order two-point boundary-value problems. Zbl 0790.65078Sloan, Ian H.; Tran, Dat; Fairweather, Graeme 9 1993 A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Zbl 1067.65135Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 8 2005 Alternating direction implicit Galerkin methods for an evolution equation with a positive-type memory term. Zbl 1328.65209Khebchareon, Morrakot; Pani, Amiya K.; Fairweather, Graeme 8 2015 A survey of higher-order methods for the numerical integration of semidiscrete parabolic problems. Zbl 0561.65087Seward, W. L.; Fairweather, G.; Johnston, R. L. 8 1984 Galerkin and collocation methods for partial integro-differential equations. Zbl 0737.65103Fairweather, G. 8 1991 Matrix decomposition algorithms for the \(C^{0}\)-quadratic finite element Galerkin method. Zbl 1176.65132Du, Kui; Fairweather, Graeme; Nguyen, Que N.; Sun, Weiwei 8 2009 Galerkin method for vibration problems in two space variables. Zbl 0246.65031Fairweather, Graeme 8 1972 Three-dimensional image reconstruction using the PF/MFS technique. Zbl 1244.65224Tankelevich, R.; Fairweather, G.; Karageorghis, A. 8 2009 An explicit extrapolated box scheme for the Gurtin-MacCamy equation. Zbl 0792.65108Fairweather, G.; López-Marcos, J. C. 7 1994 The Crank-Nicolson Hermite cubic orthogonal spline collocation method for the heat equation with nonlocal boundary conditions. Zbl 1279.80005Bialecki, B.; Fairweather, G.; López-Marcos, J. C. 7 2013 Optimal superconvergent one step nodal cubic spline collocation methods. Zbl 1091.65118Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 7 2005 Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. Zbl 0722.76073Shippy, D. J.; Kondapalli, P. S.; Fairweather, G. 7 1990 Fourier methods for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0805.65107Bialecki, Bernard; Fairweather, G.; Remington, K. A. 6 1994 On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112Robinson, M. P.; Fairweather, G.; Herbst, B. M. 6 1993 Optimal superconvergent one step quadratic spline collocation methods. Zbl 1155.65089Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q. N. 6 2008 A new alternating direction method for parabolic equations in three space variables. Zbl 0137.33302Fairweather, G.; Mitchell, A. R. 6 1965 The extrapolated Crank-Nicolson orthogonal spline collocation method for a quasilinear parabolic problem with nonlocal boundary conditions. Zbl 1309.65141Bialecki, B.; Fairweather, G.; López-Marcos, J. 5 2015 Optimal superconvergent one step quadratic spline collocation methods for Helmholtz problems. Zbl 1157.65470Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Nguyen, Que N. 5 2008 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 4 1980 An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G. 4 1994 Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Zbl 1360.76291Robinson, Mark P.; Fairweather, Graeme 4 1993 The method of fundamental solutions for problems in potential theory. Zbl 0511.65087Fairweather, Graeme; Johnston, R. L. 3 1982 Matrix decomposition algorithms for arbitrary order \(C^0\) tensor product finite element systems. Zbl 1297.65029Du, Kui; Fairweather, Graeme; Sun, Weiwei 3 2015 An investigation of Romberg quadrature. Zbl 0394.65008Fairweather, Graeme; Keast, Pat 3 1978 A survey of spline collocation methods for the numerical solution of differential equations. Zbl 0679.65058Fairweather, Graeme; Maede, Daniel 3 1989 Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Zbl 1172.65062Bialecki, Bernard; Fairweather, Graeme; Knudson, David B.; Lipman, D. Abram; Nguyen, Que N.; Sun, Weiwei; Weinberg, Gadalia M. 3 2009 Numerical integration. Recent developments, software and applications. (Proceedings of the NATO Advanced Research Workshop on Numerical Integration. Recent Developments, Software and Applications, Halifax, Canada, August 11-15, 1986). Zbl 0611.00023 3 1987 A quadratic spline collocation method for the Dirichlet biharmonic problem. Zbl 1434.65290Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Maack, Jonathan 2 2020 Direct numerical spline methods for first-order Fredholm integro- differential equations. Zbl 0799.65153Micula, Gheorghe; Fairweather, Graeme 2 1993 On the approximate solution of a diffusion problem by Galerkin methods. Zbl 0428.65062Fairweather, G. 2 1979 On the extrapolation of Galerkin methods for parabolic problems. Zbl 0282.65080Fairweather, G.; Johnson, J. P. 2 1975 Convergence analyses of Crank-Nicolson orthogonal spline collocation methods for linear parabolic problems in two space variables. Zbl 1347.65147Khebchareon, Morrakot; Pani, Amiya Kumar; Fairweather, Graeme 2 2016 The Crank-Nicolson orthogonal spline collocation method for one-dimensional parabolic problems with interfaces. Zbl 1456.65059Bhal, Santosh Kumar; Danumjaya, P.; Fairweather, G. 1 2021 Errata: Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0331.65078Dendy, J. E. jun.; Fairweather, G. 1 1976 On the \(H^{-1}\)-Galerkin method for second-order linear two-point boundary value problems. Zbl 0546.65056Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar 1 1984 On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems. Zbl 0573.65086Fairweather, G.; Saylor, A. V. 1 1983 An assessment of numerical software for solving two-point boundary-value problems arising in heat transfer. Zbl 0619.76046Fairweather, Graeme; Vedha-Nayagam, M. 1 1987 A Crank-Nicolson orthogonal spline collocation method for vibration problems. Zbl 0994.74081Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 1 2000 Remark on algorithm 603. Zbl 0645.65017Diaz, J. C.; Fairweather, G.; Keast, P. 1 1988 Finite element methods for nonlinear parabolic and hyperbolic partial integro-differential equations. Zbl 0726.65160Fairweather, Graeme; Yanik, Elizabeth G. 1 1989 Some computational results of an improved A. D. I. method for the Dirichlet problem. Zbl 0148.39404Fairweather, G.; Mitchell, A. R. 1 1966 The Crank-Nicolson orthogonal spline collocation method for one-dimensional parabolic problems with interfaces. Zbl 1456.65059Bhal, Santosh Kumar; Danumjaya, P.; Fairweather, G. 1 2021 A quadratic spline collocation method for the Dirichlet biharmonic problem. Zbl 1434.65290Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Maack, Jonathan 2 2020 Convergence analyses of Crank-Nicolson orthogonal spline collocation methods for linear parabolic problems in two space variables. Zbl 1347.65147Khebchareon, Morrakot; Pani, Amiya Kumar; Fairweather, Graeme 2 2016 An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation. Zbl 1328.65216Fairweather, Graeme; Yang, Xuehua; Xu, Da; Zhang, Haixiang 33 2015 A backward Euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation. Zbl 1352.65392Fairweather, Graeme; Zhang, Haixiang; Yang, Xuehua; Xu, Da 15 2015 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. Zbl 1352.65393Fernandes, Ryan I.; Bialecki, Bernard; Fairweather, Graeme 11 2015 Alternating direction implicit Galerkin methods for an evolution equation with a positive-type memory term. Zbl 1328.65209Khebchareon, Morrakot; Pani, Amiya K.; Fairweather, Graeme 8 2015 The extrapolated Crank-Nicolson orthogonal spline collocation method for a quasilinear parabolic problem with nonlocal boundary conditions. Zbl 1309.65141Bialecki, B.; Fairweather, G.; López-Marcos, J. 5 2015 Matrix decomposition algorithms for arbitrary order \(C^0\) tensor product finite element systems. Zbl 1297.65029Du, Kui; Fairweather, Graeme; Sun, Weiwei 3 2015 The Crank-Nicolson Hermite cubic orthogonal spline collocation method for the heat equation with nonlocal boundary conditions. Zbl 1279.80005Bialecki, B.; Fairweather, G.; López-Marcos, J. C. 7 2013 An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems. Zbl 1284.65026Fernandes, Ryan I.; Fairweather, Graeme 22 2012 Matrix decomposition algorithms for elliptic boundary value problems: A survey. Zbl 1208.65036Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 30 2011 Compact optimal quadratic spline collocation methods for the Helmholtz equation. Zbl 1218.65135Fairweather, Graeme; Karageorghis, Andreas; Maack, Jon 16 2011 ADI orthogonal spline collocation methods for parabolic partial integro-differential equations. Zbl 1191.65186Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 34 2010 Matrix decomposition algorithms for the \(C^{0}\)-quadratic finite element Galerkin method. Zbl 1176.65132Du, Kui; Fairweather, Graeme; Nguyen, Que N.; Sun, Weiwei 8 2009 Three-dimensional image reconstruction using the PF/MFS technique. Zbl 1244.65224Tankelevich, R.; Fairweather, G.; Karageorghis, A. 8 2009 Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Zbl 1172.65062Bialecki, Bernard; Fairweather, Graeme; Knudson, David B.; Lipman, D. Abram; Nguyen, Que N.; Sun, Weiwei; Weinberg, Gadalia M. 3 2009 Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term. Zbl 1160.65068Pani, Amiya Kumar; Fairweather, Graeme; Fernandes, Ryan I. 33 2008 Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations. Zbl 1168.76037Fairweather, Graeme; Ma, Heping; Sun, Weiwei 10 2008 Optimal superconvergent one step quadratic spline collocation methods. Zbl 1155.65089Bialecki, B.; Fairweather, G.; Karageorghis, A.; Nguyen, Q. N. 6 2008 Optimal superconvergent one step quadratic spline collocation methods for Helmholtz problems. Zbl 1157.65470Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas; Nguyen, Que N. 5 2008 Potential field based geometric modelling using the method of fundamental solutions. Zbl 1130.65035Tankelevich, Roman; Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 14 2006 Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods. Zbl 1388.76359Fairweather, Graeme; Lin, Qun; Lin, Yanping; Wang, Junping; Zhang, Shuhua 14 2006 A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Zbl 1067.65135Fairweather, Graeme; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis 8 2005 Optimal superconvergent one step nodal cubic spline collocation methods. Zbl 1091.65118Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 7 2005 Algorithms for almost block diagonal linear systems. Zbl 1062.65031Fairweather, Graeme; Gladwell, Ian 25 2004 The method of fundamental solutions for scattering and radiation problems. Zbl 1060.76649Fairweather, Graeme; Karageorghis, Andreas; Martin, P. A. 122 2003 Matrix decomposition algorithms for modified spline collocation for Helmholtz problems. Zbl 1035.65135Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas 11 2003 \(H^1\)-Galerkin mixed finite element methods for parabolic partial integro-differential equations. Zbl 1008.65101Pani, Amiya K.; Fairweather, Graeme 53 2002 An H\(^{1}\)-Galerkin mixed finite element method for an evolution equation with a positive-type memory term. Zbl 1047.65085Pani, Amiya K.; Fairweather, Graeme 10 2002 Discrete-time orthogonal spline collocation methods for vibration problems. Zbl 1028.74022Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 9 2002 Orthogonal spline collocation methods for partial differential equations. Zbl 0971.65105Bialecki, B.; Fairweather, G. 61 2001 The method of fundamental solutions for axisymmetric elasticity problems. Zbl 1011.74005Karageorghis, A.; Fairweather, G. 32 2000 Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. Zbl 1051.65018Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M. 17 2000 A Crank-Nicolson orthogonal spline collocation method for vibration problems. Zbl 0994.74081Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 1 2000 The method of fundamental solutions for axisymmetric potential problems. Zbl 0932.74078Karageorghis, Andreas; Fairweather, Graeme 34 1999 The method of fundamental solutions for elliptic boundary value problems. Zbl 0922.65074Fairweather, Graeme; Karageorghis, Andreas 487 1998 Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables. Zbl 0911.65095Li, Bingkun; Fairweather, Graeme; Bialecki, Bernard 26 1998 Orthogonal spline collocation methods for biharmonic problems. Zbl 0908.65103Lou, Zhou-Ming; Bialecki, Bernard; Fairweather, Graeme 10 1998 Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Zbl 0868.65068Fairweather, G.; López-Marcos, J. C. 29 1996 Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems. Zbl 0820.65009Bialecki, Bernard; Fairweather, Graeme 12 1995 Orthogonal spline collocation methods for Schrödinger-type equations in one space variable. Zbl 0806.65123Robinson, Mark P.; Fairweather, Graeme 33 1994 Spline collocation methods for a class of hyperbolic partial integro- differential equations. Zbl 0814.65137Fairweather, Graeme 30 1994 An explicit extrapolated box scheme for the Gurtin-MacCamy equation. Zbl 0792.65108Fairweather, G.; López-Marcos, J. C. 7 1994 Fourier methods for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0805.65107Bialecki, Bernard; Fairweather, G.; Remington, K. A. 6 1994 An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation. Zbl 0798.65105Bialecki, Bernard; Cai, X.-C.; Dryja, M.; Fairweather, G. 4 1994 Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0768.65067Fernandes, Ryan I.; Fairweather, Graeme 28 1993 Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Zbl 0781.65031Bialecki, Bernard; Fairweather, Graeme 19 1993 A fourth-order cubic spline method for linear second-order two-point boundary-value problems. Zbl 0790.65078Sloan, Ian H.; Tran, Dat; Fairweather, Graeme 9 1993 On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112Robinson, M. P.; Fairweather, G.; Herbst, B. M. 6 1993 Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Zbl 1360.76291Robinson, Mark P.; Fairweather, Graeme 4 1993 Direct numerical spline methods for first-order Fredholm integro- differential equations. Zbl 0799.65153Micula, Gheorghe; Fairweather, Graeme 2 1993 Orthogonal spline collocation methods for some partial integrodifferential equations. Zbl 0756.65157Yan, Yi; Fairweather, Graeme 47 1992 Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. Zbl 0752.65076Bialecki, Bernard; Fairweather, Graeme; Bennett, Karin R. 22 1992 The method of fundamental solutions for transmission and scattering of elastic waves. Zbl 0825.73150Kondapalli, Prasanna S.; Shippy, Davdi J.; Fairweather, Graeme 14 1992 The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65050Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 11 1992 Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. Zbl 0892.65051Majaess, Fouad; Keast, Patrick; Fairweather, Graeme; Bennett, Karin R. 11 1992 The reformulation and numerical solution of certain nonclassical initial- boundary value problems. Zbl 0722.65062Fairweather, Graeme; Saylor, Rick D. 32 1991 An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables. Zbl 0747.65082Fernandes, Ryan I.; Fairweather, Graeme 19 1991 A box method for a nonlinear equation of population dynamics. Zbl 0734.92023Fairweather, G.; López-Marcos, J. C. 15 1991 Galerkin and collocation methods for partial integro-differential equations. Zbl 0737.65103Fairweather, G. 8 1991 Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. Zbl 0722.76073Shippy, D. J.; Kondapalli, P. S.; Fairweather, G. 7 1990 The simple layer potential method of fundamental solutions for certain biharmonic problems. Zbl 0687.76028Karageorghis, Andreas; Fairweather, Graeme 23 1989 The method of fundamental solutions for the solution of nonlinear plane potential problems. Zbl 0676.65110Karageorghis, A.; Fairweather, G. 22 1989 A survey of spline collocation methods for the numerical solution of differential equations. Zbl 0679.65058Fairweather, Graeme; Maede, Daniel 3 1989 Finite element methods for nonlinear parabolic and hyperbolic partial integro-differential equations. Zbl 0726.65160Fairweather, Graeme; Yanik, Elizabeth G. 1 1989 Finite element methods for parabolic and hyperbolic partial integro- differential equations. Zbl 0657.65142Yanik, Elizabeth G.; Fairweather, Graeme 90 1988 The Almansi method of fundamental solutions for solving biharmonic problems. Zbl 0639.65066Karageorghis, Andreas; Fairweather, Graeme 22 1988 Remark on algorithm 603. Zbl 0645.65017Diaz, J. C.; Fairweather, G.; Keast, P. 1 1988 The method of fundamental solutions for the numerical solution of the biharmonic equation. Zbl 0618.65108Karageorghis, Andreas; Fairweather, Graeme 107 1987 Numerical integration. Recent developments, software and applications. (Proceedings of the NATO Advanced Research Workshop on Numerical Integration. Recent Developments, Software and Applications, Halifax, Canada, August 11-15, 1986). Zbl 0611.00023 3 1987 An assessment of numerical software for solving two-point boundary-value problems arising in heat transfer. Zbl 0619.76046Fairweather, Graeme; Vedha-Nayagam, M. 1 1987 Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. Zbl 0595.65122Greenwell-Yanik, C. E.; Fairweather, G. 29 1986 The method of fundamental solutions for problems in potential flow. Zbl 0546.76021Johnston, R. L.; Fairweather, G. 44 1984 A survey of higher-order methods for the numerical integration of semidiscrete parabolic problems. Zbl 0561.65087Seward, W. L.; Fairweather, G.; Johnston, R. L. 8 1984 On the \(H^{-1}\)-Galerkin method for second-order linear two-point boundary value problems. Zbl 0546.65056Fairweather, Graeme; Keast, Patrick; Diaz, Julio Cesar 1 1984 FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. Zbl 0516.65013Diaz, J. C.; Fairweather, G.; Keast, P. 61 1983 On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems. Zbl 0573.65086Fairweather, G.; Saylor, A. V. 1 1983 The method of fundamental solutions for problems in potential theory. Zbl 0511.65087Fairweather, Graeme; Johnston, R. L. 3 1982 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 4 1980 On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method. Zbl 0397.65080Fairweather, Graeme; Rizzo, Frank J.; Shippy, David J.; Wu, Yensen S. 15 1979 On the approximate solution of a diffusion problem by Galerkin methods. Zbl 0428.65062Fairweather, G. 2 1979 Finite element Galerkin methods for differential equations. Zbl 0372.65044Fairweather, Graeme 64 1978 A note on the efficient implementation of certain Padé methods for linear parabolic problems. Zbl 0384.65036Fairweather, Graeme 10 1978 An investigation of Romberg quadrature. Zbl 0394.65008Fairweather, Graeme; Keast, Pat 3 1978 Errata: Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0331.65078Dendy, J. E. jun.; Fairweather, G. 1 1976 Alternating-direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons. Zbl 0295.65062Dendy, J. E. jun.; Fairweather, G. 18 1975 On the extrapolation of Galerkin methods for parabolic problems. Zbl 0282.65080Fairweather, G.; Johnson, J. P. 2 1975 Three-level Galerkin methods for parabolic equations. Zbl 0313.65107Dupont, Todd; Fairweather, Graeme; Johnson, J. Peter 36 1974 Galerkin method for vibration problems in two space variables. Zbl 0246.65031Fairweather, Graeme 8 1972 On the eigenvalues and eigenvectors of a class of Hessenberg matrices. Zbl 0217.52603Fairweather, G. 10 1971 A new computational procedure for A.D.I. methods. Zbl 0252.65072Fairweather, G.; Mitchell, A. R. 44 1967 Some stable difference approximations to a fourth-order parabolic partial differential equation. Zbl 0147.13801Fairweather, G.; Gourlay, A. R. 18 1967 Some high accuracy difference with a Splitting operator for equations of parabolic and elliptic type. Zbl 0148.39403Fairweather, G.; Gourlay, A. R.; Mitchell, A. R. 12 1967 Some computational results of an improved A. D. I. method for the Dirichlet problem. Zbl 0148.39404Fairweather, G.; Mitchell, A. R. 1 1966 A high accuracy alternating direction method for the wave equation. Zbl 0221.65180Fairweather, G.; Mitchell, A. R. 21 1965 A new alternating direction method for parabolic equations in three space variables. Zbl 0137.33302Fairweather, G.; Mitchell, A. R. 6 1965 Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations. Zbl 0123.12001Mitchell, A. R.; Fairweather, G. 24 1964 all cited Publications top 5 cited Publications all top 5 Cited by 1,635 Authors 69 Karageorghis, Andreas 54 Xu, Da 48 Chen, Ching-Shyang 43 Chen, Wen 37 Fairweather, Graeme 31 Bialecki, Bernard 30 Lesnic, Daniel 28 Marin, Liviu 25 Dehghan Takht Fooladi, Mehdi 23 Young, Der-Liang 22 Yang, Xuehua 21 Zhang, Haixiang 20 Gu, Yan 18 Johansson, B. Tomas 18 Tsai, Chia-Cheng 17 Fan, Chia-Ming 17 Fu, Zhuojia 17 Li, Zi-Cai 17 Smyrlis, Yiorgos-Sokratis 16 Alves, Carlos J. S. 16 Lin, Ji 14 Li, Jichun 14 Pani, Amiya Kumar 13 Cheng, Alexander H.-D. 13 Qin, Qinghua 13 Wang, Fajie 12 Li, Ming 12 Qiao, Leijie 12 Qiu, Wenlin 12 Qu, Wenzhen 12 Šarler, Božidar 12 Sun, Linlin 11 Jorge, Juan Carlos 11 Sun, Weiwei 10 Kolodziej, Jan Adam 10 Shi, Dongyang 10 Wei, Ting 9 Abbasbandy, Saeid 9 Godinho, Luís M. C. 9 Liu, Xiaoyan 9 Potier-Ferry, Michel 9 Zhang, Chuanzeng 8 Bujanda, Blanca 8 Fernandes, Ryan I. 8 He, Yinnian 8 Huang, Hung-Tsai 8 Khaliq, Abdul Q. M. 8 Sapagovas, Mifodijus 8 Sinha, Rajen Kumar 8 Tadeu, António J. B. 7 Du, Kui 7 Grabski, Jakub Krzysztof 7 Hou, Tianliang 7 Li, Hong 7 Lin, Yanping 7 Liu, Yang 7 Martins, Nuno F. M. 7 Mitchell, Andrew Ronald 7 Mohanty, Ranjan Kumar 7 Ramachandran, Palghat A. 7 Reddy, Gujji Murali Mohan 7 Reeve, Thomas 7 Sun, Yao 7 Valtchev, Svilen S. 7 Wang, Hui 6 Abou-Dina, Moustafa S. 6 Antunes, Pedro Ricardo Simão 6 Boroomand, Bijan 6 Danumjaya, Palla 6 Hon, Yiu-Chung 6 Li, Xiaolin 6 Ling, Leevan 6 Liu, Chein-Shan 6 Liu, Qingguo 6 Muir, Paul H. 6 Shivanian, Elyas 6 Wang, Jinfeng 6 Wei, Xing 6 Whiteman, John Robert 6 Yang, Fenglian 6 Zhou, Zhaojie 5 Avazzadeh, Zakieh 5 Balakrishnan, Karthik 5 Berger, J. R. 5 Chen, Bin 5 Chen, Jeng-Tzong 5 Chiang, John Y. 5 Čiegis, Raimondas 5 Doha, Eid H. 5 Ganesh, Mahadevan 5 Gourlay, A. R. 5 Kaur, Deepti 5 Lee, Ming-Gong 5 Li, Junpu 5 Li, Wen 5 Li, Xin 5 Liao, Wenyuan 5 López-Marcos, Juan Carlos 5 McLean, William 5 Rashed, Youssef F. ...and 1,535 more Authors all top 5 Cited in 191 Serials 241 Engineering Analysis with Boundary Elements 97 Computers & Mathematics with Applications 93 Journal of Computational and Applied Mathematics 72 Applied Mathematics and Computation 56 Applied Numerical Mathematics 53 Journal of Computational Physics 43 International Journal of Computer Mathematics 41 Numerical Methods for Partial Differential Equations 37 Computer Methods in Applied Mechanics and Engineering 34 Numerical Algorithms 30 Journal of Scientific Computing 30 Applied Mathematical Modelling 22 Inverse Problems in Science and Engineering 22 Advances in Applied Mathematics and Mechanics 21 Mathematics and Computers in Simulation 20 Numerische Mathematik 20 Advances in Computational Mathematics 19 Mathematics of Computation 16 Computational Mechanics 14 International Journal for Numerical Methods in Engineering 14 Computational and Applied Mathematics 13 Journal of Applied Mathematics and Computing 12 Applied Mathematics Letters 10 Mathematical Problems in Engineering 9 Applicable Analysis 9 BIT 9 Computing 9 Mathematical and Computer Modelling 8 Journal of Mathematical Analysis and Applications 8 Journal of Integral Equations and Applications 8 Mathematical Modelling and Analysis 8 International Journal of Computational Methods 7 SIAM Journal on Numerical Analysis 7 SIAM Journal on Scientific Computing 7 Advances in Difference Equations 6 International Journal for Numerical Methods in Fluids 6 Calcolo 6 Communications in Numerical Methods in Engineering 6 Communications in Computational Physics 5 Computers and Fluids 5 Wave Motion 5 Numerical Functional Analysis and Optimization 5 Acta Mathematicae Applicatae Sinica. 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Real World Applications 4 International Journal of Numerical Analysis and Modeling 4 Journal of Function Spaces 3 Archive for Rational Mechanics and Analysis 3 International Journal of Heat and Mass Transfer 3 International Journal of Solids and Structures 3 Journal of Fluid Mechanics 3 Journal of Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Chaos, Solitons and Fractals 3 Applied Mathematics and Optimization 3 International Journal of Mathematics and Mathematical Sciences 3 Japan Journal of Industrial and Applied Mathematics 3 Applications of Mathematics 3 Computational Mathematics and Mathematical Physics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Discrete Dynamics in Nature and Society 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Discrete and Continuous Dynamical Systems. 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Physical Sciences 2 Journal of Applied Mathematics 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Mediterranean Journal of Mathematics 2 Discrete and Continuous Dynamical Systems. Series S 2 Advances in Mathematical Physics 2 International Journal of Differential Equations 2 Afrika Matematika 2 Nonlinear Analysis. Theory, Methods & Applications ...and 91 more Serials all top 5 Cited in 38 Fields 1,230 Numerical analysis (65-XX) 678 Partial differential equations (35-XX) 199 Mechanics of deformable solids (74-XX) 166 Fluid mechanics (76-XX) 147 Integral equations (45-XX) 64 Classical thermodynamics, heat transfer (80-XX) 46 Ordinary differential equations (34-XX) 40 Optics, electromagnetic theory (78-XX) 29 Biology and other natural sciences (92-XX) 27 Real functions (26-XX) 25 Approximations and expansions (41-XX) 21 Potential theory (31-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 12 Geophysics (86-XX) 11 Systems theory; control (93-XX) 9 Integral transforms, operational calculus (44-XX) 9 Probability theory and stochastic processes (60-XX) 8 Functions of a complex variable (30-XX) 8 Operator theory (47-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Statistics (62-XX) 6 Quantum theory (81-XX) 6 Operations research, mathematical programming (90-XX) 5 Combinatorics (05-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-XX) 4 Special functions (33-XX) 4 Computer science (68-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Difference and functional equations (39-XX) Citations by Year