Edit Profile (opens in new tab) Butcher, John C. Compute Distance To: Compute Author ID: butcher.john-c Published as: Butcher, J. C.; Butcher, John C.; Butcher, John more...less Further Spellings: Butcher, John Charles Homepage: https://www.math.auckland.ac.nz/~butcher/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef Documents Indexed: 159 Publications since 1956, including 5 Books 6 Contributions as Editor · 2 Further Contributions Reviewing Activity: 43 Reviews Biographic References: 2 Publications Co-Authors: 47 Co-Authors with 67 Joint Publications 884 Co-Co-Authors all top 5 Co-Authors 96 single-authored 14 Jackiewicz, Zdzislaw 5 Cash, Jeff R. 5 Chartier, Philippe 4 Chan, T. M. H. 4 Podhaisky, Helmut 3 Burrage, Kevin 3 Chen, D. J. L. 3 Hill, Adrian T. 3 Imran, Gulshad 2 Abdi, Ali 2 Chan, Robert Peng Kong 2 Chipman, F. H. 2 Diamantakis, M. T. 2 Norton, Terence J. T. 2 van der Houwen, Pieter J. 2 Wanner, Gerhard 1 Ahmad, Saghir 1 Baker, Christopher Thomas Hale 1 Brezinski, Claude 1 Cooper, Gavin J. 1 Corless, Robert Malcolm 1 D’Ambrosio, Raffaele 1 Delves, L. M. 1 Elhay, Sylvan 1 Enright, Wayne H. 1 Gander, Martin Jakob 1 Gautschi, Walter 1 Gladwell, Ian 1 Gonzalez-Vega, Laureano 1 Habib, Yousaf 1 Heard, A. D. 1 Henell, M. A. 1 Hewitt, L. L. 1 Hojjati, Gholamreza 1 Johnston, P. B. 1 Kautsky, Jaroslav 1 Lambert, J. D. 1 Lorentzen, Lisa 1 Mazzia, Francesca 1 Messel, Harry 1 Milovanović, Gradimir V. 1 Mittelmann, Hans Detlef 1 Miyatake, Yuto 1 Moir, Nicolette 1 Moore, Gerald 1 O’Sullivan, A. E. 1 Prothero, A. 1 Rabinowitz, Philip 1 Rattenbury, Nicolette 1 Robertson, H. N. 1 Russell, Robert D. 1 Sameh, Ahmed H. 1 Sanz-Serna, Jesús María 1 Sehnalová, Pavla 1 Shakoori, Azar 1 Singh, Adit D. 1 Söderling, G. 1 Sweatman, Winston L. 1 Tracogna, S. 1 Wait, R. 1 Watt, J. M. 1 Weiner, Rüdiger all top 5 Serials 27 Applied Numerical Mathematics 24 Numerical Algorithms 22 BIT 10 Mathematics of Computation 7 SIAM Journal on Numerical Analysis 6 Journal of Computational and Applied Mathematics 5 BIT. Nordisk Tidskrift for Informationsbehandling 3 IMA Journal of Numerical Analysis 3 Computing 3 Journal of the Association for Computing Machinery 3 Journal of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 ACM Transactions on Mathematical Software 2 Numerische Mathematik 2 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 Biometrika 1 Bulletin of the London Mathematical Society 1 The Computer Journal. Section A / Section B 1 The Fibonacci Quarterly 1 Mathematics and Computers in Simulation 1 Journal of Complexity 1 Journal of Scientific Computing 1 Linear Algebra and its Applications 1 Bulletin. The Institute of Mathematics and its Applications 1 The Canadian Applied Mathematics Quarterly 1 Computational and Applied Mathematics 1 Advances in Computational Mathematics 1 The Arabian Journal for Science and Engineering. Section C: Theme Issues 1 The ANZIAM Journal 1 Acta Numerica 1 Nuclear Physics 1 Springer Series in Computational Mathematics 1 Axioms 1 Contemporary Mathematicians all top 5 Fields 149 Numerical analysis (65-XX) 104 Ordinary differential equations (34-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 General and overarching topics; collections (00-XX) 7 History and biography (01-XX) 4 Combinatorics (05-XX) 3 Number theory (11-XX) 3 Approximations and expansions (41-XX) 2 Mechanics of particles and systems (70-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 143 Publications have been cited 3,950 times in 2,234 Documents Cited by ▼ Year ▼ The numerical analysis of ordinary differential equations. Runge-Kutta and general linear methods. Zbl 0616.65072Butcher, J. C. 586 1987 Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041Butcher, J. C. 343 2008 Implicit Runge-Kutta processes. Zbl 0123.11701Butcher, J. C. 222 1964 Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004Butcher, J. C. 176 2016 Numerical methods for ordinary differential equations. Zbl 1040.65057Butcher, J. C. 155 2003 Stability criteria for implicit Runge-Kutta methods. Zbl 0396.65043Burrage, Kevin; Butcher, J. C. 131 1979 Coefficients for the study of Runge-Kutta integration processes. Zbl 0223.65031Butcher, J. C. 121 1963 An algebraic theory of integration methods. Zbl 0258.65070Butcher, J. C. 121 1972 Non-linear stability of a general class of differential equation methods. Zbl 0431.65051Burrage, Kevin; Butcher, J. C. 115 1980 On the implementation of implicit Runge-Kutta methods. Zbl 0336.65037Butcher, J. C. 96 1976 On Runge-Kutta processes of high order. Zbl 0244.65046Butcher, J. C. 86 1964 Modern numerical methods for ordinary differential equations. Zbl 0348.65064 84 1976 Some numerical methods for stiff problems. Zbl 1032.65512Butcher, J. C. 77 2003 On the convergence of numerical solutions to ordinary differential equations. Zbl 0141.13504Butcher, J. C. 77 1966 Diagonally-implicit multi-stage integration methods. Zbl 0773.65046Butcher, J. C. 75 1993 A stability property of implicit Runge-Kutta methods. Zbl 0333.65031Butcher, J. C. 65 1975 An implementation of singly-implicit Runge-Kutta methods. Zbl 0456.65040Burrage, K.; Butcher, J. C.; Chipman, F. H. 64 1980 General linear methods. Zbl 1113.65072Butcher, J. C. 59 2006 The order of numerical methods for ordinary differential equations. Zbl 0278.65073Butcher, J. C. 56 1973 Second derivative methods with RK stability. Zbl 1084.65069Butcher, J. C.; Hojjati, G. 48 2005 Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043Butcher, J. C.; Jackiewicz, Z. 47 1993 Integration processes based on Radau quadrature formulas. Zbl 0123.11702Butcher, J. C. 46 1964 The construction of practical general linear methods. Zbl 1046.65054Butcher, J. C.; Wright, W. M. 44 2003 A modified multistep method for the numerical integration of ordinary differential equations. Zbl 0125.07102Butcher, J. C. 42 1965 Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044Butcher, J. C.; Jackiewicz, Z. 41 1997 Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056Butcher, J. C.; Jackiewicz, Z. 36 1996 Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080Butcher, J. C.; Jackiewicz, Z. 36 1998 An iteration scheme for implicit Runge-Kutta methods. Zbl 0525.65052Cooper, G. J.; Butcher, J. C. 33 1983 A transformed implicit Runge-Kutta method. Zbl 0439.65057Butcher, J. C. 29 1979 On the attainable order of Runge-Kutta methods. Zbl 0132.36401Butcher, J. C. 25 1965 A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232Miyatake, Yuto; Butcher, John C. 24 2016 The control of parasitism in \(G\)-symplectic methods. Zbl 1309.65148Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T. 23 2014 The effective order of Runge-Kutta methods. Zbl 0185.41301Butcher, J. C. 23 1969 Trees and numerical methods for ordinary differential equations. Zbl 1184.65072Butcher, J. C. 22 2010 Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077Butcher, J. C.; Tracogna, S. 22 1997 Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 22 1999 Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083Butcher, J. C.; Jackiewicz, Z. 21 2004 A history of Runge-Kutta methods. Zbl 0858.65073Butcher, J. C. 20 1996 General linear methods for stiff differential equations. Zbl 0983.65085Butcher, J. C. 20 2001 Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063Butcher, J. C. 19 2000 Nordsieck representation of DIMSIMs. Zbl 0920.65043Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 18 1997 A multistep generalization of Runge-Kutta methods with four or five stages. Zbl 0168.13901Butcher, J. C. 18 1967 Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068Butcher, J. C.; Jackiewicz, Z.; Wright, W. M. 16 2007 A new approach to error estimation for general linear methods. Zbl 1032.65088Butcher, J. C.; Jackiewicz, Z. 16 2003 A nonlinear optimization approach to the construction of general linear methods of high order. Zbl 0879.65051Butcher, J. C.; Jackiewicz, Z.; Mittelmann, H. D. 15 1997 Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078Butcher, J. C.; Jackiewicz, Z. 15 2004 ARK methods for stiff problems. Zbl 1070.65059Butcher, John C.; Rattenbury, Nicolette 15 2005 The equivalence of algebraic stability and AN-stability. Zbl 0637.65083Butcher, J. C. 14 1987 A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058Butcher, J. C.; Chen, D. J. L. 14 2000 Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072Butcher, J. C.; Cash, J. R. 14 1990 Trees, B-series and exponential integrators. Zbl 1185.65121Butcher, J. C. 13 2010 Runge-Kutta methods: Some historical notes. Zbl 0867.65038Butcher, J. C.; Wanner, G. 13 1996 The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089Butcher, J. C.; Chartier, P. 13 1999 On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080Butcher, J. C.; Podhaisky, H. 12 2006 On A-stable implicit Runge-Kutta methods. Zbl 0378.65039Butcher, J. C. 12 1977 DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064Butcher, J. C.; Diamantakis, M. T. 12 1998 A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081Butcher, J. C.; Jackiewicz, Z. 11 2001 DESI methods for stiff initial-value problems. Zbl 0884.65077Butcher, J. C.; Cash, J. R.; Diamantakis, M. T. 11 1996 Stability of numerical methods for ordinary differential equations. Zbl 1016.65059Butcher, J. C.; Heard, A. D. 11 2002 The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040Butcher, J. C. 10 1992 Order and stability of generalized Padé approximations. Zbl 1182.65111Butcher, J. C. 10 2009 The non-existence of ten stage eighth order explicit Runge-Kutta methods. Zbl 0579.65066Butcher, J. C. 10 1985 An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085Butcher, J. C. 10 1997 A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076Butcher, J. C.; Chartier, P. 10 1997 General linear methods. Zbl 0874.65057Butcher, J. C. 10 1996 Order bounds for second derivative approximations. Zbl 1247.65103Abdi, A.; Butcher, J. C. 10 2012 Linear and non-linear stability for general linear methods. Zbl 0623.65074Butcher, J. C. 10 1987 Towards efficient implementation of singly-implicit methods. Zbl 0639.65041Butcher, J. C. 10 1988 A generalization of singly-implicit methods. Zbl 0484.65048Butcher, J. C. 10 1981 The existence of symplectic general linear methods. Zbl 1176.65080Butcher, J. C.; Hewitt, L. L. 10 2009 A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048Butcher, J. C.; Wright, W. M. 10 2003 Linear multistep methods as irreducible general linear methods. Zbl 1102.65078Butcher, J. C.; Hill, A. T. 9 2006 Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272Butcher, John C.; D’Ambrosio, Raffaele 9 2017 General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059Butcher, J. C. 9 1993 High order A-stable numerical methods for stiff problems. Zbl 1203.65106Butcher, J. C. 8 2005 Thirty years of G-stability. Zbl 1105.65085Butcher, J. C. 8 2006 Symmetric general linear methods. Zbl 1355.65095Butcher, J. C.; Hill, A. T.; Norton, T. J. T. 8 2016 General linear method: A survey. Zbl 0619.65057Butcher, J. C. 8 1985 On the integration processes of A. Huta. Zbl 0223.65032Butcher, J. C. 8 1963 The \(A\)-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057Butcher, J. C. 8 2002 The adaptation of STRIDE to delay differential equations. Zbl 0776.65049Butcher, J. C. 7 1992 Applications of doubly companion matrices. Zbl 1089.65065Butcher, J. C.; Wright, W. M. 7 2006 Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar 7 2011 Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068Butcher, J. C. 7 2013 On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119Butcher, J. C. 7 2009 A transformation for the analysis of DIMSIMs. Zbl 0814.65079Butcher, J. C. 7 1994 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039Butcher, J. C.; Sanz-Serna, J. M. 7 1996 Generalized Padé approximations to the exponential function. Zbl 0789.65063Butcher, J. C.; Chipman, F. H. 7 1992 Some implementation schemes for implicit Runge-Kutta methods. Zbl 0447.65042Butcher, J. C. 7 1980 Error estimation for Nordsieck methods. Zbl 1012.65083Butcher, J. C.; Jackiewicz, Z. 7 2002 Forty-five years of A-stability. Zbl 1191.65109Butcher, J. C. 6 2009 Order and stability of parallel methods for stiff problems. Zbl 0884.65090Butcher, J. C. 6 1997 B-series. Algebraic analysis of numerical methods. Zbl 07332820Butcher, John C. 6 2021 Random sampling from the normal distribution. Zbl 0094.13503Butcher, J. C. 6 1961 Defect correction for two-point boundary value problems on nonequidistant meshes. Zbl 0828.65102Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D. 5 1995 Parallel general linear methods for stiff ordinary differential and differential algebraic equations. Zbl 0833.65073Butcher, J. C.; Chartier, P. 5 1995 Applications of order arrows. Zbl 1241.65070Abdi, A.; Butcher, J. C. 5 2012 Optimal order and stepsize sequences. Zbl 0615.65076Butcher, J. C. 5 1986 An order bound for Runge-Kutta methods. Zbl 0318.65030Butcher, J. C. 5 1975 An application of the Runge-Kutta space. Zbl 0555.65045Butcher, J. C. 5 1984 Isomeric trees and the order of Runge-Kutta methods. Zbl 1492.65202Butcher, John C.; Podhaisky, Helmut 1 2022 B-series. Algebraic analysis of numerical methods. Zbl 07332820Butcher, John C. 6 2021 Trees, stumps, and applications. Zbl 1432.65087Butcher, John C. 1 2018 Partitioned general linear methods for separable Hamiltonian problems. Zbl 1365.65272Butcher, John C.; D’Ambrosio, Raffaele 9 2017 A G-symplectic method with order 6. Zbl 1367.65190Butcher, John C.; Imran, Gulshad; Podhaisky, Helmut 4 2017 Numerical methods for ordinary differential equations. 3rd edition. Zbl 1354.65004Butcher, J. C. 176 2016 A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems. Zbl 1342.65232Miyatake, Yuto; Butcher, John C. 24 2016 Symmetric general linear methods. Zbl 1355.65095Butcher, J. C.; Hill, A. T.; Norton, T. J. T. 8 2016 Order conditions for G-symplectic methods. Zbl 1338.65185Butcher, John C.; Imran, Gulshad 4 2015 The cohesiveness of G-symplectic methods. Zbl 1330.65192Butcher, J. C. 4 2015 Runge-Kutta methods for ordinary differential equations. Zbl 1330.65109Butcher, J. C. 1 2015 The control of parasitism in \(G\)-symplectic methods. Zbl 1309.65148Butcher, John C.; Habib, Yousaf; Hill, Adrian T.; Norton, Terence J. T. 23 2014 Symplectic effective order methods. Zbl 1291.65359Butcher, John C.; Imran, Gulshad 4 2014 Walter Gautschi, Volume 3. Selected works with commentaries. Edited by Claude Brezinski and Ahmed Sameh. Zbl 1292.01007Gautschi, Walter 1 2014 Dealing with parasitic behaviour in G-symplectic integrators. Zbl 1263.65068Butcher, J. C. 7 2013 Predictor-corrector Obreshkov pairs. Zbl 1307.65099Butcher, John C.; Sehnalová, Pavla 3 2013 Order bounds for second derivative approximations. Zbl 1247.65103Abdi, A.; Butcher, J. C. 10 2012 Applications of order arrows. Zbl 1241.65070Abdi, A.; Butcher, J. C. 5 2012 Polynomial algebra for Birkhoff interpolants. Zbl 1218.41002Butcher, John C.; Corless, Robert M.; Gonzalez-Vega, Laureano; Shakoori, Azar 7 2011 Trees and numerical methods for ordinary differential equations. Zbl 1184.65072Butcher, J. C. 22 2010 Trees, B-series and exponential integrators. Zbl 1185.65121Butcher, J. C. 13 2010 The tree and forest spaces with applications to initial-value problem methods. Zbl 1205.65211Butcher, J. C.; Chan, T. M. H. 3 2010 B-series and B-series coefficients. Zbl 1432.65096Butcher, J. C. 1 2010 Order and stability of generalized Padé approximations. Zbl 1182.65111Butcher, J. C. 10 2009 The existence of symplectic general linear methods. Zbl 1176.65080Butcher, J. C.; Hewitt, L. L. 10 2009 On fifth and sixth order explicit Runge-Kutta methods: order conditions and order barriers. Zbl 1229.65119Butcher, J. C. 7 2009 Forty-five years of A-stability. Zbl 1191.65109Butcher, J. C. 6 2009 General linear methods for ordinary differential equations. Zbl 1159.65333Butcher, John 4 2009 Practical Runge-Kutta methods for scientific computation. Zbl 1178.65083Butcher, J. C. 4 2009 Numerical methods for ordinary differential equations. 2nd revised ed. Zbl 1167.65041Butcher, J. C. 343 2008 Error propagation of general linear methods for ordinary differential equations. Zbl 1131.65068Butcher, J. C.; Jackiewicz, Z.; Wright, W. M. 16 2007 General linear methods. Zbl 1113.65072Butcher, J. C. 59 2006 On error estimation in general linear methods for stiff ODEs. Zbl 1089.65080Butcher, J. C.; Podhaisky, H. 12 2006 Linear multistep methods as irreducible general linear methods. Zbl 1102.65078Butcher, J. C.; Hill, A. T. 9 2006 Thirty years of G-stability. Zbl 1105.65085Butcher, J. C. 8 2006 Applications of doubly companion matrices. Zbl 1089.65065Butcher, J. C.; Wright, W. M. 7 2006 Second derivative methods with RK stability. Zbl 1084.65069Butcher, J. C.; Hojjati, G. 48 2005 ARK methods for stiff problems. Zbl 1070.65059Butcher, John C.; Rattenbury, Nicolette 15 2005 High order A-stable numerical methods for stiff problems. Zbl 1203.65106Butcher, J. C. 8 2005 Construction of general linear methods with Runge-Kutta stability properties. Zbl 1055.65083Butcher, J. C.; Jackiewicz, Z. 21 2004 Unconditionally stable general linear methods for ordinary differential equations. Zbl 1066.65078Butcher, J. C.; Jackiewicz, Z. 15 2004 Numerical methods for ordinary differential equations. Zbl 1040.65057Butcher, J. C. 155 2003 Some numerical methods for stiff problems. Zbl 1032.65512Butcher, J. C. 77 2003 The construction of practical general linear methods. Zbl 1046.65054Butcher, J. C.; Wright, W. M. 44 2003 A new approach to error estimation for general linear methods. Zbl 1032.65088Butcher, J. C.; Jackiewicz, Z. 16 2003 A transformation relating explicit and diagonally-implicit general linear methods. Zbl 1016.65048Butcher, J. C.; Wright, W. M. 10 2003 Experiments with a new fifth order method. Zbl 1030.65081Butcher, John C.; Moir, Nicolette 2 2003 Stability of numerical methods for ordinary differential equations. Zbl 1016.65059Butcher, J. C.; Heard, A. D. 11 2002 The \(A\)-stability of methods with Padé and generalized Padé stability functions. Zbl 1016.65057Butcher, J. C. 8 2002 Error estimation for Nordsieck methods. Zbl 1012.65083Butcher, J. C.; Jackiewicz, Z. 7 2002 A new approach to the algebraic structures for integration methods. Zbl 1016.65047Butcher, J. C.; Chan, T. M. H. 2 2002 Nordsieck methods with an off-step point. Zbl 1012.65074Butcher, J. C.; O’Sullivan, A. E. 2 2002 Special issue: Numerical methods for ordinary differential equations (ANODE 2001), Auckland, New Zealand, January 8–12, 2001. Selected papers. Zbl 1017.00022 1 2002 General linear methods for stiff differential equations. Zbl 0983.65085Butcher, J. C. 20 2001 A reliable error estimation for diagonally implicit multistage integration methods. Zbl 0998.65081Butcher, J. C.; Jackiewicz, Z. 11 2001 On the implementation of ESIRK methods for stiff IVPs. Zbl 0974.65075Butcher, J. C.; Chen, D. J. L. 3 2001 Variable stepsize schemes for effective order methods and enhanced order composition methods. Zbl 0976.65067Butcher, J. C.; Chan, T. M. H. 2 2001 Numerical methods for ordinary differential equations in the 20th century. Zbl 0969.65063Butcher, J. C. 19 2000 A new type of singly-implicit Runge-Kutta method. Zbl 0954.65058Butcher, J. C.; Chen, D. J. L. 14 2000 The choice of parameters in parallel general linear methods for stiff problems. Zbl 0949.65076Butcher, J. C.; Singh, A. D. 2 2000 Multi-step zero approximations for stepsize control. Zbl 0951.65072Butcher, J. C.; Chan, T. M. H. 2 2000 Experiments with a variable-order type 1 DIMSIM code. Zbl 0958.65083Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 22 1999 The effective order of singly-implicit Runge-Kutta methods. Zbl 0936.65089Butcher, J. C.; Chartier, P. 13 1999 Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0933.65080Butcher, J. C.; Jackiewicz, Z. 36 1998 DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. Zbl 0908.65064Butcher, J. C.; Diamantakis, M. T. 12 1998 Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Zbl 0899.65048Butcher, J. C.; Chan, R. P. K. 5 1998 Order and effective order. Zbl 0927.65095Butcher, J. C. 5 1998 ESIRK methods and variable stepsize. Zbl 0927.65096Butcher, J. C.; Chen, D. J. L. 3 1998 ARK methods up to order five. Zbl 0907.65069Butcher, J. C. 2 1998 Implementation of diagonally implicit multistage integration methods for ordinary differential equations. Zbl 0892.65044Butcher, J. C.; Jackiewicz, Z. 41 1997 Order conditions for two-step Runge-Kutta methods. Zbl 0906.65077Butcher, J. C.; Tracogna, S. 22 1997 Nordsieck representation of DIMSIMs. Zbl 0920.65043Butcher, J. C.; Chartier, P.; Jackiewicz, Z. 18 1997 A nonlinear optimization approach to the construction of general linear methods of high order. Zbl 0879.65051Butcher, J. C.; Jackiewicz, Z.; Mittelmann, H. D. 15 1997 An introduction to “Almost Runge-Kutta” methods. Zbl 0905.65085Butcher, J. C. 10 1997 A generalization of singly-implicit Runge-Kutta methods. Zbl 0906.65076Butcher, J. C.; Chartier, P. 10 1997 Order and stability of parallel methods for stiff problems. Zbl 0884.65090Butcher, J. C. 6 1997 Numerical methods for differential equations and applications. Zbl 0912.65064Butcher, J. C. 1 1997 Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations. Zbl 0865.65056Butcher, J. C.; Jackiewicz, Z. 36 1996 A history of Runge-Kutta methods. Zbl 0858.65073Butcher, J. C. 20 1996 Runge-Kutta methods: Some historical notes. Zbl 0867.65038Butcher, J. C.; Wanner, G. 13 1996 DESI methods for stiff initial-value problems. Zbl 0884.65077Butcher, J. C.; Cash, J. R.; Diamantakis, M. T. 11 1996 General linear methods. Zbl 0874.65057Butcher, J. C. 10 1996 The number of conditions for a Runge-Kutta method to have effective order \(p\). Zbl 0867.65039Butcher, J. C.; Sanz-Serna, J. M. 7 1996 Defect correction for two-point boundary value problems on nonequidistant meshes. Zbl 0828.65102Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D. 5 1995 Parallel general linear methods for stiff ordinary differential and differential algebraic equations. Zbl 0833.65073Butcher, J. C.; Chartier, P. 5 1995 On fifth order Runge-Kutta methods. Zbl 0837.65073Butcher, J. C. 3 1995 An introduction to DIMSIMs. Zbl 0838.65078Butcher, J. C. 1 1995 A transformation for the analysis of DIMSIMs. Zbl 0814.65079Butcher, J. C. 7 1994 Initial value problems: Numerical methods and mathematics. Zbl 0817.65059Butcher, J. C. 2 1994 Some orbital test problems. Zbl 0806.65068Butcher, J. C. 1 1994 Diagonally-implicit multi-stage integration methods. Zbl 0773.65046Butcher, J. C. 75 1993 Diagonally implicit general linear methods for ordinary differential equations. Zbl 0795.65043Butcher, J. C.; Jackiewicz, Z. 47 1993 General linear methods for the parallel solution of ordinary differential equations. Zbl 0834.65059Butcher, J. C. 9 1993 The role of orthogonal polynomials in numerical ordinary differential equations. Zbl 0768.65040Butcher, J. C. 10 1992 The adaptation of STRIDE to delay differential equations. Zbl 0776.65049Butcher, J. C. 7 1992 Generalized Padé approximations to the exponential function. Zbl 0789.65063Butcher, J. C.; Chipman, F. H. 7 1992 Some new hybrid methods for initial value problems. Zbl 0769.65037Butcher, J. C. 2 1992 On symmetrizers for Gauss method. Zbl 0723.65045Butcher, J. C.; Chan, R. P. K. 2 1992 Towards efficient Runge-Kutta methods for stiff systems. Zbl 0702.65072Butcher, J. C.; Cash, J. R. 14 1990 Order, stepsize and stiffness switching. Zbl 0719.65059Butcher, J. C. 4 1990 ...and 43 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,568 Authors 76 Butcher, John C. 75 Jackiewicz, Zdzislaw 38 Abdi, Ali 37 Weiner, Rüdiger 32 Tsitouras, Charalampos 31 Hojjati, Gholamreza 30 D’Ambrosio, Raffaele 25 Ismail, Fudziah Bt. 25 Kulikov, Gennady Yur’evich 24 Paternoster, Beatrice 23 Senu, Norazak 22 Izzo, Giuseppe 21 Burrage, Kevin 21 You, Xiong 20 Hairer, Ernst 19 Cash, Jeff R. 19 Simos, Theodore E. 19 Spijker, Marc N. 18 Podhaisky, Helmut 18 Sanz-Serna, Jesús María 17 Li, Shoufu 17 Ramos, Higinio 17 van der Houwen, Pieter J. 16 González-Pinto, Severiano 16 Montijano, Juan Ignacio 16 Sandu, Adrian 16 Wu, Xinyuan 15 Schmitt, Bernhard A. 15 Zennaro, Marino 14 Brugnano, Luigi 14 Cong, Nguyen Huu 14 Famelis, Ioannis Th. 14 Wanner, Gerhard 13 Fang, Yonglei 13 Ketcheson, David I. 13 Li, Jiyong 13 Sommeijer, Ben P. 13 Zhang, Chengjian 13 Zlatev, Zahari 12 Chartier, Philippe 12 Ikhile, Monday Ndidi Oziegbe 12 Rández, Luis 11 Braś, Michał 11 Cooper, Gavin J. 11 Hundsdorfer, Willem H. 11 Van Daele, Marnix 11 Xiao, Aiguo 10 Calvo, Manuel 10 Chan, Robert Peng Kong 10 Evans, David John 10 Huang, Chengming 10 Manchon, Dominique 10 Munthe-Kaas, Hans Z. 10 Wang, Wansheng 9 Cardone, Angelamaria 9 Conte, Dajana 9 Gottlieb, Sigal 9 Hill, Adrian T. 9 Iavernaro, Felice 9 Nørsett, Syvert Paul 9 Scherer, Rudolf 9 Tian, Hongjiong 9 Vanden Berghe, Guido 9 Vermiglio, Rossana 9 Verner, James H. 8 Corless, Robert Malcolm 8 Debrabant, Kristian 8 Faragó, István 8 Ibrahim, Zarina Bibi Binti 8 Kvaerno, Anne 8 Lubich, Christian 8 Magherini, Cecilia 8 Schneid, Josef 8 Wang, Zhongqing 8 Wen, Liping 8 Yu, Yuexin 7 Bellen, Alfredo 7 Blanes, Sergio 7 De Meyer, Hans E. 7 Dormand, John R. 7 Ebrahimi-Fard, Kurusch 7 Havasi, Ágnes 7 Iserles, Arieh 7 Kraaijevanger, J. F. B. M. 7 Martín-Vaquero, Jesús 7 Mitsui, Taketomo 7 Moradi, Afsaneh 7 Murugesan, K. 7 Murugesh, V. 7 Nakashima, Masaharu 7 Okuonghae, Robert I. 7 Ostermann, Alexander 7 Prince, P. J. 7 Ranocha, Hendrik 7 Tang, Wensheng 7 Vaillancourt, Rémi 7 Verwer, Jan G. 6 Axelsson, Axel Owe Holger 6 Băleanu, Dumitru I. 6 Bartoszewski, Zbigniew ...and 2,468 more Authors all top 5 Cited in 298 Serials 253 Applied Numerical Mathematics 214 Journal of Computational and Applied Mathematics 141 Journal of Computational Physics 130 Applied Mathematics and Computation 130 BIT 91 Numerical Algorithms 71 Computers & Mathematics with Applications 55 International Journal of Computer Mathematics 53 Journal of Scientific Computing 52 Mathematics of Computation 51 Numerische Mathematik 39 Computing 36 Computer Methods in Applied Mechanics and Engineering 34 BIT. Nordisk Tidskrift for Informationsbehandling 29 SIAM Journal on Scientific Computing 25 Journal of Mathematical Chemistry 22 Computers and Fluids 22 Computer Physics Communications 22 Computational and Applied Mathematics 20 Mathematics and Computers in Simulation 20 SIAM Journal on Numerical Analysis 19 Calcolo 17 Applied Mathematics Letters 16 Journal of Applied Mathematics and Computing 14 Applied Mathematical Modelling 14 Mathematical Problems in Engineering 13 Advances in Computational Mathematics 13 Foundations of Computational Mathematics 11 Japan Journal of Industrial and Applied Mathematics 10 Communications in Nonlinear Science and Numerical Simulation 9 Chaos, Solitons and Fractals 9 Mathematical and Computer Modelling 9 Advances in Difference Equations 8 Discrete Dynamics in Nature and Society 7 Journal of the Nigerian Mathematical Society 7 Linear Algebra and its Applications 7 Journal of Applied Mathematics 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 International Journal of Applied and Computational Mathematics 6 Computational Mathematics and Mathematical Physics 6 Celestial Mechanics and Dynamical Astronomy 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 6 Discrete and Continuous Dynamical Systems 6 Abstract and Applied Analysis 5 Journal of Fluid Mechanics 5 International Journal for Numerical Methods in Engineering 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Bulletin of the Iranian Mathematical Society 5 Chaos 5 Discrete and Continuous Dynamical Systems. Series B 5 Mediterranean Journal of Mathematics 5 Communications in Computational Physics 5 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Theoretical Biology 5 Axioms 5 Communications on Applied Mathematics and Computation 4 Acta Mechanica 4 Communications in Mathematical Physics 4 Journal of Mathematical Analysis and Applications 4 Physica A 4 Advances in Mathematics 4 Automatica 4 Physica D 4 Journal of Difference Equations and Applications 4 Nonlinear Dynamics 4 International Journal of Modern Physics C 4 Mathematical Modelling and Analysis 4 Computational Methods in Applied Mathematics 4 International Journal of Computational Methods 4 Symmetry 4 Afrika Matematika 4 Statistics and Computing 3 Journal of the Franklin Institute 3 Journal of Mathematical Physics 3 Physics Letters. A 3 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 3 Annals of the Institute of Statistical Mathematics 3 The Annals of Probability 3 Journal of Computer and System Sciences 3 Journal of Optimization Theory and Applications 3 Numerical Functional Analysis and Optimization 3 Acta Applicandae Mathematicae 3 Optimization 3 Computational Mechanics 3 The Annals of Applied Probability 3 Applications of Mathematics 3 Celestial Mechanics 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Computers and Mathematics with Applications. Part A 3 Monte Carlo Methods and Applications 3 Optimization Methods & Software 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 SIAM Journal on Applied Dynamical Systems 3 Computational & Mathematical Methods in Medicine 3 Advances in Applied Mathematics and Mechanics 2 International Journal of Control 2 International Journal of Mathematical Education in Science and Technology 2 Indian Journal of Pure & Applied Mathematics 2 Information Processing Letters ...and 198 more Serials all top 5 Cited in 55 Fields 1,899 Numerical analysis (65-XX) 877 Ordinary differential equations (34-XX) 263 Partial differential equations (35-XX) 181 Fluid mechanics (76-XX) 118 Dynamical systems and ergodic theory (37-XX) 104 Probability theory and stochastic processes (60-XX) 81 Biology and other natural sciences (92-XX) 61 Mechanics of particles and systems (70-XX) 54 Integral equations (45-XX) 49 Systems theory; control (93-XX) 47 Mechanics of deformable solids (74-XX) 45 Computer science (68-XX) 41 Quantum theory (81-XX) 40 Approximations and expansions (41-XX) 35 Combinatorics (05-XX) 31 Associative rings and algebras (16-XX) 31 Operations research, mathematical programming (90-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 21 Statistics (62-XX) 21 Statistical mechanics, structure of matter (82-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Optics, electromagnetic theory (78-XX) 15 Classical thermodynamics, heat transfer (80-XX) 15 Information and communication theory, circuits (94-XX) 14 Geophysics (86-XX) 13 Nonassociative rings and algebras (17-XX) 12 Operator theory (47-XX) 11 History and biography (01-XX) 11 Real functions (26-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Difference and functional equations (39-XX) 6 Differential geometry (53-XX) 5 Number theory (11-XX) 5 Category theory; homological algebra (18-XX) 5 Topological groups, Lie groups (22-XX) 5 Relativity and gravitational theory (83-XX) 4 General and overarching topics; collections (00-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral transforms, operational calculus (44-XX) 4 Astronomy and astrophysics (85-XX) 3 Special functions (33-XX) 3 Functional analysis (46-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Functions of a complex variable (30-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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