AN EFFICIENT NUMERICAL TECHNIQUE FOR SOLVING HEAT EQUATION WITH NONLOCAL BOUNDARY CONDITIONS

Year 2022, Volume: 6 Issue: 2, 157 - 167, 30.06.2022

Zakia Hammouch , Anam Zahra Azız Rehman Syed Ali Mardan

https://doi.org/10.31197/atnaa.846217

Cited By: 1

Abstract

A third order parallel algorithm is proposed 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 develop here is tested on two model problems. We conclude that our method provides better accuracy due to availability of real arithmetic.

Keywords

Parabolic partial differential equation, Non-local boundary conditions, Finite difference scheme, Integral boundary condition.

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