The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions

DOI10.1145/146847.146926zbMath0892.65050OpenAlexW2158782543WikidataQ113310566 ScholiaQ113310566MaRDI QIDQ4371795

Fouad Majaess, Karin R. Bennett, Graeme Fairweather, Patrick Keast

Publication date: 9 February 1998

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: http://www.acm.org/pubs/contents/journals/toms/1992-18/

zbMATH Keywords

boundary value problemsimplicit Runge-Kutta methodsmultiple shootingB-spline basisalmost block diagonal systemsalternate column and row pivoting algorithmspline collocation at Gaussian points

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Nonlinear boundary value problems for ordinary differential equations (34B15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Radial basis functions based meshfree schemes for the simulation of non-linear extended Fisher-Kolmogorov model, Orthogonal cubic spline collocation method for the Cahn-Hilliard equation, Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation, A fourth–order orthogonal spline collocation method for two‐dimensional Helmholtz problems with interfaces, The Crank-Nicolson orthogonal spline collocation method for one-dimensional parabolic problems with interfaces, Fourth order orthogonal spline collocation methods for two-point boundary value problems with interfaces, High-order orthogonal spline collocation methods for two-point boundary value problems with interfaces, An alternating direction implicit method for orthogonal spline collocation linear systems, Unnamed Item, Orthogonal spline collocation methods for partial differential equations, Orthogonal cubic spline collocation method for the extended Fisher--Kolmogorov equation, Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions, Almost block diagonal linear systems: sequential and parallel solution techniques, and applications, ABDPACK

Uses Software

• SOLVEBLOK
• LINPACK
• COLROW
• ARCELO