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

  • Syed Ali Mardan Department of Mathematics, University of Management and Technology, CII, Johar Town, Lahore-54590, Pakistan
  • Zakia Hammouch Department of Mathematics, University of Management and Technology, CII, Johar Town, Lahore-54590, Pakistan
  • Muhammad Aziz ur Rehman Department of Mathematics, School of Sciences, University of Management and Technology, Lahore, Pakistan
  • Kanwal Tariq Department of Mathematics Faculty of Sciences and Techniques, Moulay Ismail Meknes Morocco
DOI: https://doi.org/10.32350/sir/22/020206
Keywords: parabolic partial differential equation, non-local boundary conditions, finite difference scheme, integral boundary condition

Abstract

Abstract Views: 104

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.

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Published
2018-04-30
How to Cite
1.
Syed Ali Mardan, Zakia Hammouch, Muhammad Aziz ur Rehman, Kanwal Tariq. Third Order Parallel Splitting Method for Nonhomogeneous Heat Equation with Integral Boundary Conditions. Sci Inquiry Rev. [Internet]. 2018Apr.30 [cited 2024Nov.27];2(2):68-1. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/317
Issue
Vol 2 No 2: April 2018
Section
Orignal Article

Copyright (c) 2019 Syed Ali Mardan, Zakia Hammouch, Muhammad Aziz ur Rehman, Kanwal Tariq

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This work is licensed under a Creative Commons Attribution 4.0 International License.