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A Wavelet Method for the Solution of Nonlinear Integral Equations with Singular Kernels

Jizeng Wang1,2, Lei Zhang1, Youhe Zhou1
Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education of China, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu, 730000, China.
Corresponding author. E-mail: jzwang@lzu.edu.cn

Computer Modeling in Engineering & Sciences 2014, 102(2), 127-148. https://doi.org/10.3970/cmes.2014.102.127

Abstract

In this paper, we propose an efficient wavelet method for numerical solution of nonlinear integral equations with singular kernels. The proposed method is established based on a function approximation algorithm in terms of Coiflet scaling expansion and a special treatment of boundary extension. The adopted Coiflet bases in this algorithm allow each expansion coefficient being explicitly expressed by a single-point sampling of the function, which is crucially important for dealing with nonlinear terms in the equations. In addition, we use the technique of integration by parts to transform the original integral equations with non-smooth or singular kernels into regular ones with smooth kernels. Then, we incorporate the proposed function approximation algorithm into the Galerkin method for the solution of the transformed nonlinear integral equations. Numerical examples show that the proposed wavelet method is much more accurate and efficient than several others.

Keywords

Coilfet, wavelet Galerkin method, nonlinear integral equations, singular kernel

Cite This Article

Wang, J., Zhang, L., Zhou, Y. (2014). A Wavelet Method for the Solution of Nonlinear Integral Equations with Singular Kernels. CMES-Computer Modeling in Engineering & Sciences, 102(2), 127–148.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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