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Geometric mesh FDM for self-adjoint singular perturbation boundary value problems. (English) Zbl 1124.65064

The authors propose a numerical method for second order singularly perturbed self-adjoint two-point boundary value problems, based on the finite difference method (FDM) with variable mesh. The original problem is reduced to its normal form and the reduced problem is solved by the FDM taking a variable mesh (geometric mesh). Numerical examples are also provided.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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