Numerical treatment of singularity perturbed two point boundary value problems
Applied Mathematics and Computation
Singular perturbation methods for ordinary differential equations
Singular perturbation methods for ordinary differential equations
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The present paper is concerned with the approximate analytic series solution of the nonlinear two-point second-order singularly perturbed boundary value problems. In place of the traditional numerical, perturbation or asymptotic methods, a homotopy technique is employed. It is shown that proper choices of an auxiliary linear operator and also an initial approximation during the implementation of the homotopy analysis method (HAM) can yield uniformly valid and accurate solutions. The fast convergence of the method is ensured by the optimal convergence control parameter obtained through the absolute residual error concept. To demonstrate the favor of the HAM over the traditional finite-difference techniques several nonlinear problems have been solved and compared.