Numerical solution of two-dimensional Fredholm–Hammerstein integral equations on 2D irregular domains by using modified moving least-square method

Abstract

In this work, we describe a numerical scheme based on modified moving least-square (MMLS) method for solving Fredholm–Hammerstein integral equations on 2D irregular domains. The moment matrix in moving least squares (MLS) method may be singular when the number of points in the local support domain is not enough. To overcome this problem, the MMLS method with non-singular moment matrix is used. The basic advantage of the proposed method does not require any adaptation of the nodal density in non-rectangular domain and the results converge more quickly to the exact solution. The error bound for the proposed method is provided. The new technique is examined in various integral equations and compared with the classical MLS method to show the accuracy and computational efficiency of the method.

Keywords:

• Moving least-squares approximation
• modified moving least-square approximation
• 2D irregular domains
• Fredholm–Hammerstein integral equations
• Gauss–Legendre quadrature
• quadratic and cubic spline weight functions
• convergence analysis

2010 Mathematics Subject Classifications:

• 65R20
• 45A05
• 45G10

Disclosure statement

No potential conflict of interest was reported by the author(s).