The discrete collocation method for Fredholm–Hammerstein integral equations based on moving least squares method

Abstract

The purpose of this paper is to investigate the discrete collocation method based on moving least squares (MLS) approximation for Fredholm–Hammerstein integral equations. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. Error analysis of this method is also investigated. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.

Keywords:

• Fredholm–Hammerstein integral equations
• moving least squares method
• Meshless method
• error analysis
• numerical treatment

2010 AMS Subject Classification:

• 45G10

Disclosure statement

No potential conflict of interest was reported by the authors.