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Zbl 1130.65082
Natesan, Srinivasan; Deb, Briti Sundar
A Robust computational method for singularly perturbed coupled system of reaction-diffusion boundary-value problems. (English)
[J] Appl. Math. Comput. 188, No. 1, 353-364 (2007). ISSN 0096-3003

The authors devise a robust computational method for singularly perturbed systems of reaction-diffusion boundary-value problems on a piecewise uniform Shishkin mesh on the whole domain. They prove that this newly proposed scheme is uniformly stable throughout the domain and provides second-order uniform convergence results, and give a test problem to verify the efficiency and accuracy of the method.
[Ziwen Jiang (Shandong)]

MSC 2000:: *65L20 Stability of numerical methods for ODE
65L10 Boundary value problems for ODE (numerical methods)
65L12 Finite difference methods for ODE
34B15 Nonlinear boundary value problems of ODE
34E15 Asymptotic singular perturbations, general theory (ODE)
65L50 Mesh generation and refinement (ODE)

Keywords: singular perturbation; boundary layers; cubic spline; piecewise-uniform Shishkin mesh; uniform convergence; stability; numerical examples; system of reaction-diffusion boundary-value problems

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