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An initial-value approach for solving singularly perturbed two-point boundary value problems. (English) Zbl 1058.65079

Summary: An initial-value approach is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. This approach is based on the boundary layer behavior of the solution. The method is distinguished by the following fact: The given singularly perturbed two-point boundary value problem is replaced by three first order initial-value problems. Several linear and non-linear problems are solved to demonstrate the applicability of the method. It is observed that the present method approximates the exact solution very well.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
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References:

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