Modified Method for Parabolic Equations in one Dimensional with Nonlocal time Weighting Initial Condition

Abstract

In this paper, we develop a modified version of explicit scheme based on finite difference method for the one-dimensional parabolic partial differential equations with nonlocal time weighting initial conditions. The dominancy of the Saulyev’s schemes based on finite difference, over the previous explicit FTCS, Duke-Frankel, as well as implicit BTCS, Crandal’s technique and Crank Nicholson’s scheme has already been established, which proved to be unconditionally stable, use less CPU time and computational effort. However, in this paper a modification of Saulyev’s first kind formula is developed. Main focus was to reduce error of the Saulyev’s formula using proposed method. The comparison has been carried out between both methods to observe errors in different conditions and step sizes. The new modified scheme is proved to be satisfactory and unconditionally stable.