Non-standard methods for singularly perturbed problems possessing oscillatory/layer solutions

DOI10.1016/j.amc.2006.09.011zbMath1128.65060OpenAlexW2049679050MaRDI QIDQ883935

Kailash C. Patidar, Jean M.-S. Lubuma

Publication date: 12 June 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.09.011

zbMATH Keywords

maximum principleconvergencenumerical resultsboundary value problemssingular perturbationsnonstandard finite difference methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12)

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Cites Work

• A survey of numerical techniques for solving singularly perturbed ordinary differential equations
• Contributions to the mathematics of the nonstandard finite difference method and applications
• Calculation of oscillatory properties of the solutions of two coupled, first order non-linear ordinary differential equations
• NONSTANDARD FINITE DIFFERENCE METHODS
• CONTRIBUTIONS TO THE THEORY OF NON-STANDARD FINITE DIFFERENCE METHODS AND APPLICATIONS TO SINGULAR PERTURBATION PROBLEMS
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator
• On the use of nonstandard finite difference methods†
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