ABDPACK swMATH ID: 1221 Software Authors: Fouad Majaess , Patrick Keast , Graeme Fairweather , Karin R. Bennett Description: 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: ABDPACK is a package of FORTRAN programs for the solution of systems of linear equations with the almost block diagonal structure arising in spline collocation at Gaussian points with monomial spline basis functions, when applied to two-point boundary value problems with separated boundary conditions. The package ABBPACK is designed to handle a subclass of such linear systems which have what may be called an almost block bidiagonal structure. Such systems result, for example, when condensation is applied to the full spline collocation linear system. This package may also be used to solve the almost block bidiagonal systems arising in multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems. The algorithms implemented in the package are based on an alternate column and row pivoting scheme which avoids most of the fill-in introduced by more commonly used techniques. Homepage: http://portal.acm.org/citation.cfm?id=146927 Related Software: COLROW; ARCELO; RODAS; SOLVEBLOK; COLNEW; PDECOL; ELLPACK; Matlab; PMIRKDC; BABDCR; MIRKDC; PDECHEB; EPDCOL; GELDA; LINPACK Cited in: 15 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year 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. 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. 1992 all top 5 Cited by 19 Authors 7 Fairweather, Graeme 4 Danumjaya, Palla 3 Bialecki, Bernard 2 Bennett, Karin R. 2 Bhal, Santosh Kumar 2 Keast, Patrick 2 Majaess, Fouad 2 Manickam, S. Arul Veda 2 Pani, Amiya Kumar 2 Sharma, Vishnu Dutt 1 Amodio, Pierluigi 1 Gladwell, Ian 1 Jiwari, Ram 1 Madhumita, G. 1 Manickam, A. V. 1 Mittal, Ramesh Chand 1 Moudgalya, Kannan M. 1 Radha, Ch. 1 Romanazzi, Giuseppe all top 5 Cited in 10 Serials 4 Journal of Computational and Applied Mathematics 3 ACM Transactions on Mathematical Software 1 Computers & Mathematics with Applications 1 Wave Motion 1 Applied Mathematics and Computation 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 SIAM Review 1 Nonlinear Dynamics all top 5 Cited in 6 Fields 13 Numerical analysis (65-XX) 7 Partial differential equations (35-XX) 3 Ordinary differential equations (34-XX) 3 Fluid mechanics (76-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) Citations by Year