An asymptotic-numerical method for singularly perturbed Robin problems-I

摘要

In this paper, singularly perturbed Robin type problem for second-order ordinary differential equations (ODEs) is considered. Here an asymptotic-numerical method is suggested for this type of problems. In this method, an asymptotic approximate solution and solution obtained by a numerical method which involves an exponentially fitted difference (EFD) scheme are combined suitably to yield solution of the present problem. More precisely, a `transition point' is chosen inside the interval of integration where the solution of the reduced problem is evaluated which will be taken as a boundary value for the `boundary layer' region (inner region) problem. We perform iteration here by moving the transition point towards right-hand side slowly until the solution gets stabilized. In the outer region (rest of the interval) the solution of the reduced problem is taken as an approximation to the original problem. Error estimates are provided and numerical examples are presented.