Cubic spline method for a class of nonlinear singularly-perturbed boundary-value problems
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In this paper, we present a numerical method for solving a class of nonlinear, singularly perturbed two-point boundary-value problems with a boundary layer on the left end of the underlying interval. The original second-order problem is reduced to an asymptotically equivalent first-order problem and is solved by a numerical method using a fourth-order cubic spline in the inner region. The method has been analyzed for convergence and is shown to yield anO(h4) approximation to the solution. Some test examples have been solved to demonstrate the efficiency of the method.
Key WordsSingularly-perturbed boundary-value problems boundary layers cubic splines singularly-perturbed initial-value problems nonasymptotic methods
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