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Robust monotone iterates for nonlinear singularly perturbed boundary value problems. (English) Zbl 1177.65107

Summary: This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving the nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.

MSC:

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
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

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