Robust higher order finite difference scheme for singularly perturbed turning point problem with two outflow boundary layers

In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution to this class of turning point problem possesses two outflow exponential boundary layers. Parameter-explicit theoretical bounds on the analytical solution derivatives are given, which are used in the error analysis of the proposed scheme. A hybrid finite difference scheme discretizes the problem comprising of midpoint-upwind and central difference operator on an appropriate piecewise-uniform fitted mesh. An error analysis has been carried out for the proposed scheme by splitting the solution into regular and singular components, and the method has been shown to be second-order uniformly convergent except for a logarithmic factor with respect to the singular perturbation parameter. Some relevant numerical examples are also illustrated to verify the theoretical aspects computationally. Numerical experiments show that the proposed method gives competitive results compared to those of other methods available in the literature.