A highly stable deferred correction scheme with interpolant for systems of nonlinear two-point boundary value problems

DOI10.1016/S0377-0427(02)00873-7zbMath1019.65052MaRDI QIDQ1811594

N. Sumarti, Marnix van Daele, Jeff R. Cash, Daniel R. Moore

Publication date: 17 June 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

interpolationalgorithmsstabilitysystemserror estimatessuperconvergenceimplicit Runge-Kutta methodRichardson extrapolationstiff problemsnonlinear two-point boundary value problemsdeferred correctionLobatto formulaeMIRK code TWPBVP.f

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm

Uses Software

• twpbvp

Cites Work

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• Error estimation and iterative improvement for discretization algorithms
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• An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
• An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems
• Some improvements in the use of relaxation methods for the solution of ordinary and partial differential equations