Spline-based parameter-uniform scheme for fourth-order singularly perturbed differential equations

Abstract

This paper considers a numerical study for the fourth-order singularly perturbed boundary value problems. The associated differential equation is converted into a weakly coupled system of two singularly perturbed ordinary differential equations with Dirichlet boundary conditions to solve the problem numerically. In the system, one of the equations is independent of the perturbation parameter. To solve this system, we present a numerical technique of quadratic B-splines on an exponentially graded mesh. The established results show that the scheme is second-order uniformly convergent in the discrete maximum norm. The theoretical results are validated using the proposed method on two test problems.