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An asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations. (English) Zbl 1040.65071

The authors consider numerical methods for the approximate solution of a second-order singularly perturbed linear boundary value problem for ordinary differential equations. They transform of the original problem into simpler initial and terminal value problems, and apply exponentially fitted finite difference schemes to calculate the approximate singularly perturbed solutions. Error estimates and numerical examples are provided to illustrate the method, which appears to be appropriate for parallel computing.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65Y05 Parallel numerical computation
65L12 Finite difference and finite volume methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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