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

Open Access

Original research article

Author(s):

Zakia Hammouch^a, Anam Zahra^b, Aziz Rehman^c, Syed Ali Mardan^c

^a Department of Mathematics, Faculty of Sciences and Techniques, Moulay Ismail Meknes, Morocco.
^b Department of Mathematics, Virtual University, 54 Lawrence Road, Lahore, Pakistan.
^c Department of Mathematics, University of the Management and Technology, C-II, Johar Town, Lahore-54590, Pakistan.

Advances in the Theory of Nonlinear Analysis and its Applications 6(2), 157-167.

Received: December 24, 2020

Accepted: January 8, 2022

Published: January 13, 2022

Abstract

A fourth-order parallel splitting algorithm is proposed to solve one-dimensional non-homogeneous heat equation with integral boundary conditions. We approximate the space derivative by fourth-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.

Keywords: Finite difference scheme, Method of lines, Padé’s approximation, Simpson’s 1/3, Partial differential equation, Boundary condition, Initial conditions.

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APA Style

Hammouch, Z., Zahra, A., Rehman, A., & Mardan, S. A. AN EFFICIENT NUMERICAL TECHNIQUE FOR SOLVING HEAT EQUATION WITH NONLOCAL BOUNDARY CONDITIONS. Advances in the Theory of Nonlinear Analysis and its Application, 6(2), 157-167.