Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 239, Issue -, Pages 72-92Publisher
ELSEVIER
DOI: 10.1016/j.cam.2012.09.010
Keywords
Nonlinear integral equation; Two-dimensional integral equation; Radial basis functions (RBFs); Meshless method; Non-rectangular domains; Error analysis
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In this paper, we present a numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on a non-rectangular domain. The method utilizes radial basis functions (RBFs) constructed on scattered points as a basis in the discrete collocation method. The proposed scheme is meshless, since it does not need any domain element and so it is independent of the geometry of the domain. The method reduces the solution of the two-dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations. Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of the new technique. (C) 2012 Elsevier B.V. All rights reserved.
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