Finite Integration Method Using Chebyshev Expansion for Solving Nonlinear Poisson Equations on Irregular Domains

A. Duangpan1 and R. Boonklurb2

1,2Department of Mathematics and Computer Science, Faculty of Science,
Chulalongkorn University, Bangkok 10330, Thailand

Received 27 March, 2019; accepted in revised form 28 April, 2020

Abstract: Several boundary value problems are de ned on complex shaped domains, such as pentagonal, circular, L-shaped, butter y, peanut-shaped and elliptic domains. These irregular domains give di culty in term of solving both analytically and numerically. This paper devises the nite integration method via Chebyshev polynomials (FIM-CBS) to deduce the e cient numerical scheme for solving two-dimensional nonlinear Poisson equations over these irregular domains with the discretization through Chebyshev nodes. The demonstrative numerical examples are provided. The numerical solutions by the FIM-CBS are compared with the analytical solutions. The results show that the proposed method is very e ective and accurate with a small number of computational nodes.

c 2020 European Society of Computational Methods in Sciences and Engineering

Keywords: nite integration method, Chebyshev polynomial, nonlinear Poisson equation, irregular domain
Mathematics Subject Classi cation: 65D30, 65M50, 65N30

 

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