Optimal cubic spline method for convection diffusion equation

Abstract

In the proposed work, we present a new collocation technique based on cubic splines to solve initial-boundary value parabolic partial differential equation. To attain fourth order accuracy, the proposed method requires only three spatial grid points as compare to the requirement of five grid points in the literature, using the collocation methods based on splines. We have used two stage Gauss Legendre method in time direction. An analysis has been done to prove the unconditional stability of the technique. To show the better accuracy of our method, numerical experiments are done by taking some examples from the literature. The results obtained, show the efficiency and the order of accuracy of the technique.