Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems

An accelerated fitted mesh scheme is proposed for the numerical solution of the singularly perturbed boundary value problems whose solution exhibits an interior layer near the turning point. To resolve the interior layer, a mesh of the Shishkin type is used with the help of a transition parameter that separates the layer and regular region. A tridiagonal solver is implemented to solve the system of equation. The stability of the described scheme is analyzed, and the truncation error is obtained. The proposed scheme is of almost second-order convergent and accelerated to almost sixth-order convergent by applying the Richardson extrapolation technique. The numerical results obtained by the present scheme have been compared with some existing methods, and it is observed that it gives better accuracy.