The impact of Legendre wavelet collocation method on the solutions of nonlinear system of two-dimensional integral equations

Abstract

Numerical solutions of nonlinear system of two-dimensional integral equations have been rarely investigated in the literature. In this study, we suggest a numerically practical algorithm to approximate the solutions of nonlinear system of two-dimensional Volterra–Fredholm and Volterra integral equations. This scheme is based on two-dimensional Legendre wavelet to reduce these nonlinear systems of integral equations to a system of nonlinear algebraic equations. The main characteristic of this approach is high accuracy and computational efficiency of performing which are the consequences of Legendre wavelet properties. The main benefit of this basic function is their ability to detect singularities and their efficiency in dealing with non-sufficiently smooth function in comparison with Legendre polynomials and they minimize the error. The convergence analysis and error bound of the proposed Legendre wavelet method is investigated. Numerical examples confirm that the Legendre wavelet collocation method is accurate, reliable for solving nonlinear system of two-dimensional integral equations.

Keywords:

• Two-dimensional legendre wavelet
• nonlinear system of two-dimensional integral equations
• collocation method
• convergence analysis

2010 Mathematics Subject Classifications:

• 65Rxx
• 45Gxx

Acknowledgments

The authors of this article expresses his sincere thanks to the learned reviewers for their valuable comments and suggestions for the improvement of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.