Nonpolynomial Spline for Numerical Solution of Singularly Perturbed Convection-Diffusion Equations with Discontinuous Source Term

Abstract

This research addresses the numerical solution of singularly perturbed convection-diffusion kind boundary value problem of second-order with a discontinuity term. Due to the perturbation parameter and discontinuity term, the problem solution has a boundary layer and an interior layer. A nonpolynomial cubic spline method is utilized to solve the boundary value problem. A specific set of parameters associated with nonpolynomial spline is used to tailor the method. A comprehensive analysis of the stability and convergence of the recommended method is presented which gives second-order convergence results. The suggested method is implemented on two examples, and the obtained results are contrasted with an existing method, highlighting the precision and efficacy of the proposed method, which would enhance the method's novelty.