A finite difference method for a numerical solution of elliptic boundary value problems-Reference-Cited by-同舟云学术

A finite difference method for a numerical solution of elliptic boundary value problems

Published:2018-06-01 Issue:1 Volume:3 Page:311-320
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Pandey P.K.¹,Jaboob S.S.A.²

Affiliation:

1. Department of Mathematics , Dyal Singh College (Univ. of Delhi) , Lodhi Road , New Delhi - 110003 , India

2. Ministry of Higher Education, Sultanate of Oman , Muscat , Oman

Abstract

Abstract In this article, we have considered for numerical solution of a Poisson and Laplace equation in a domain. we have presented a novel finite difference method for solving the system of the boundary value problems subject to Dirichlet boundary conditions. We have derived the solution of the Poisson and Laplace equations in a two-dimensional finite region. We present numerical experiments to demonstrate the efficiency of the method.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.21042/AMNS.2018.1.00024

Reference12 articles.

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2. Jomma, Z. and Macaskill, C., The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions. J. Comput. Phys. 202, 488-506 (2005). 10.1016/j.jcp.2004.07.011

3. Gibou, F., Fedkiw, R. P., Cheng, L. T. and Kang, M., A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. Journal of Computational Physics, 176(1), 205-227 (2002). 10.1006/jcph.2001.6977

4. Ng, Y. T., Chen, H., Min, C. and Gibou, F., Guidelines for poisson solvers on irregular domains with Dirichlet boundary conditions using the ghost fluid method. J. Sci. Comput. 41, 300-320 (2009). 10.1007/s10915-009-9299-8

5. Al-Said, E. A., Numerical solutions for system of third-order boundary value problems. International Journal of Computer Mathematics, Vol. 78, no. 1, 111-121 (2001). 10.1080/00207160108805100

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