A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters

Abstract

A numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings.