Derivation of finite difference methods by interpolation and collocation

DOI10.1007/s13370-012-0093-7zbMath1302.65169OpenAlexW2024701624MaRDI QIDQ467940

J. Herrera, Sumit K. Garg

Publication date: 5 November 2014

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-012-0093-7

zbMATH Keywords

interpolationcomparison of methodsfinite difference methodnumerical examplescontinuous solutionsinitial value problemAdams-Moulton methodsstability intervalserror constantmultistep collocationnonstiff problem

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (1)

A Collocation Method for Direct Numerical Integration of Initial Value Problems in Higher Order Ordinary Differential Equations

Cites Work

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• New algorithms for the continuous approximate solution of ordinary differential equations and the upgrading of the order of the processes
• A Collocation Method for Direct Numerical Integration of Initial Value Problems in Higher Order Ordinary Differential Equations
• On One-Leg Multistep Methods
• One-Step Collocation: Uniform Superconvergence, Predictor-Corrector Method, Local Error Estimate
• Superconvergence for Multistep Collocation
• Some relationships between implicit Runge-Kutta, collocation and Lanczosτ methods, and their stability properties

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