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.
Discussion(0)
No comments yet. Be the first to comment.