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

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:6 Issue:2
AN EFFICIENT NUMERICAL TECHNIQUE FOR SOLVING HEAT EQUATION WITH NONLOCAL BOUNDARY CONDITIONS

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

Authors : Zakia HAMMOUCH, Anam ZAHRA, Azız REHMAN, Syed Ali MARDAN

Pages : 157-167

Doi:10.31197/atnaa.846217

View : 11 | Download : 8

Publication Date : 2022-06-30

Article Type : Research Paper

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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