A robust, exponentially fitted higher-order numerical method for a two-parameter singularly perturbed boundary value problem

Source abstract

This study constructs a robust higher-order fitted operator finite difference method for a two-parameter singularly perturbed boundary value problem. The derivatives in the governing ordinary differential equation are substituted by second-order central finite difference approximations, after which the fitting parameter is introduced and determined. The resulting system of linear equations may then be solved using the Thomas method. The stability, consistency, and convergence of the current method have been thoroughly validated. To enhance accuracy and achieve a higher-order numerical solution, a post-processing technique was employed to upgrade the method from second-order to fourth-order convergence. Finally, three test examples were used to confirm the method's appropriateness. The numerical results demonstrate that the proposed technique is stable, consistent, and produces a higher-order numerical solution than the existing ones in the literature.