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