Wilson wavelets-based approximation method for solving nonlinear Fredholm–Hammerstein integral equations

ABSTRACT

Some of mathematical physics models deal with nonlinear integral equations such as diffraction problems, scattering in quantum mechanics, conformal mapping and etc. In fact, analytically solving such nonlinear integral equations is usually difficult, therefore, it is necessary to propose proper numerical methods. In this paper, an efficient and accurate computational method based on the Wilson wavelets and collocation method is proposed to solve a class of nonlinear Fredholm–Hammerstein integral equations. In the proposed method, Kumar and Sloan scheme is used. Convergence of the Wilson expansion is investigated and also the error analysis of the proposed method is proved. Some numerical examples are provided to demonstrate the accuracy and efficiency of the method.

KEYWORDS:

• Wilson wavelets
• Fredholm–Hammerstein integral equations
• error analysis

2010 AMS CLASSIFICATION:

• 42C40
• 65T60
• 65R20

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

F. Abdollahi http://orcid.org/0000-0001-5855-2527