- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 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 : 4 | Download : 1
Publication Date : 2022-06-30
Article Type : Research
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.