An optimal algorithm for certain boundary value problem

DOI10.1016/S0377-0427(97)00098-8zbMath0888.65090OpenAlexW1981323996MaRDI QIDQ1372105

Tadeusz Styś, Krystyna Styś

Publication date: 4 June 1998

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(97)00098-8

zbMATH Keywords

finite difference schemeerror boundsystemoptimal algorithmMathematica module

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

A difference method for solving parabolic equations of order 2\(n\) ⋮ A higher accuracy finite difference method for an elliptic equation of order four. ⋮ A numerical approach to nonlinear two-point boundary value problems for ODEs ⋮ A higher-order finite difference method for solving a system of integro-differential equations ⋮ Replacing the finite difference methods for nonlinear two-point boundary value problems by successive application of the linear shooting method ⋮ A third-order finite difference method on a quasi-variable mesh for nonlinear two point boundary value problems with Robin boundary conditions

Uses Software

• Mathematica

Cites Work

• High-order P-stable multistep methods
• Explicit two-step methods with minimal phase-lag for the numerical integration of special second-order initial-value problems and their application to the one-dimensional Schrödinger equation
• An explicit four-step phase-fitted method for the numerical integration of second-order initial-value problems
• O(h\({}^ 4)\) locally overconvergent semidiscrete scheme for the equation \(u_ t=u_{xx}+f(t,x,u)\)
• High-accuracy P-stable Methods for y^″ = f(t, y)
• On a Finite Difference Analogue of an Elliptic Boundary Problem which is Neither Diagonally Dominant Nor of Non‐negative Type
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