Third Order Parallel Splitting Method for Nonhomogeneous Heat Equation with Integral Boundary Conditions

Abstract

A third order parallel algorithm is proposed in this article to solve one dimensional non-homogenous heat equation with integral boundary conditions. For this purpose, we approximate the space derivative by third order finite difference approximation. This parallel splitting technique is combined with Simpson’s 1/3 rule to tackle the nonlocal part of this problem. The algorithm developed here is tested on two model problems. We conclude that our method provides better accuracy due to the availability of real arithmetic.