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Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers. (English) Zbl 1033.65061

The aim of this paper is to provide a layer resolving parameter uniform convergent numerical method for the turning point problem. The authors suggest an appropriate piecewise-uniform mesh and apply the classical finite-difference schemes on this mesh. The \(\varepsilon\)-uniform error estimates are derived and some numerical examples are included to support the theoretical estimates.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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References:

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