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A Robust computational method for singularly perturbed coupled system of reaction-diffusion boundary-value problems. (English) Zbl 1130.65082
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.

MSC:
65L20Stability and convergence of numerical methods for ODE
65L10Boundary value problems for ODE (numerical methods)
65L12Finite difference methods for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)
65L50Mesh generation and refinement (ODE)
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References:
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