Non-polynomial spline solution of one dimensional singularly perturbed parabolic equations

Abstract

In this paper, two-parameter singularly perturbed parabolic equations are examined by two level method using non-polynomial spline. We have used non-polynomial quadratic spline in space and finite difference discretization in time. Stability analysis is carried out. The approximate solution is shown to converge point-wise to the true solution. Numerical solution of singularly perturbed parabolic equations consisting of linear as well as non-linear has been solved. Three numerical examples are presented to show the efficiency and effectiveness of the developed method