Journal of Ocean Engineering and Science

Volume 3, Issue 4

(7)Iterative algorithm for parabolic and hyperbolic PDEs with nonlocal boundary conditions

N.A. Al-Zaid ^∗, H.O. Bakodah

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Received 1 July 2018; received in revised form 24 September 2018; accepted 11 October 2018

Available online 5 November 2018

Abstract

In this paper, we are concerned with the numerical solutions for the parabolic and hyperbolic partial differential equations with nonlocal boundary conditions. Thus, we presented a new iterative algorithm based on the Restarted Adomian Decomposition Method (RADM) for solving the two equations of different types involving dissimilar boundary and nonlocal conditions. The algorithm presented transforms the given nonlocal initial boundary value problem to a local Dirichlet one and then employs the RADM for the numerical treatment. Numerical comparisons were made between our proposed method and the Adomian Decomposition Method (ADM) to demonstrate the efﬁciency and performance of the proposed method.

This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Keywords: Adomian Decomposition Method; Restarted method; Parabolic and hyperbolic PDEs; Nonlocal boundary conditions.