Abstract
A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Finally, numerical examples are presented to show the validity and efficiency of the technique.
Highlights
Many problems of mathematical physics can be stated in the form of integral equations
Several simple and accurate methods based on orthogonal basic functions, including wavelets, have been used to approximate the solution of integral equation 1–5
Mathematical Problems in Engineering methods have been proposed for numerical solution of these types of integral equation
Summary
Many problems of mathematical physics can be stated in the form of integral equations. Mathematical Problems in Engineering methods have been proposed for numerical solution of these types of integral equation. Babolian and Delves describe an augmented Galerkin technique for the numerical solution of first kind Fredholm integral equations. Haar wavelets have been applied to solve Fredholm integral equations of first kind in. The main purpose of this article is to present a numerical method for solving 1.1 via Chebyshev wavelets. We will notice that these wavelets make the wavelet coefficient matrices sparse which concludes the sparsity of the coefficients matrix of obtained system This system may be solved by using an appropriate numerical method.
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