On the numerical solution of Fredholm integral equations utilizing the local radial basis function method. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Assari, Pouria; Asadi-Mehregan, Fatemeh; Dehghan, Mehdi
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 7(2019)
• Page Start: 1416
• Page End: 1443
• Publication Date: 2019-07-03
• Subjects: Local radial basis function -- Fredholm integral equation -- discrete collocation method -- meshless method -- error analysis; 41A25 -- 31B10 -- 45B05 -- 65R20; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1500693
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: The current investigation describes a computational technique to solve one- and two-dimensional Fredholm integral equations of the second kind. The method estimates the solution using the discrete collocation method by combining locally supported radial basis functions (RBFs) constructed on a small set of nodes instead of all points over the analysed domain. In this work, we employ the Gauss–Legendre integration rule on the influence domains of shape functions to approximate the local integrals appearing in the method. In comparison with the globally supported RBFs for solving integral equations, the proposed method is stable and uses much less computer memory. The scheme does not require any cell structures, so it is meshless. We also obtain the error analysis of the proposed method and demonstrate that the convergence rate of the approach is high. Illustrative examples clearly show the reliability and efficiency of the new method.