ABSTRACT

In literature, numerical solutions for the singular integral equation in unbounded domain are rarely investigated. The main motivation of this study is to propose a practical matrix method based on Laguerre functions to approximate the solution of this integral equation. Laguerre functions which are obtained from the Laguerre polynomials are used to avoid fluctuations for large values. The main characteristic of the scheme is good accuracy with two basis functions and less computational cost which are the consequences of Laguerre functions properties and its dual operational matrix. This matrix is equal to the identity matrix which simplify the approximation procedure and reduce the computational error of the scheme. In this technique, dual operational matrix, matrix forms and collocation method are employed to convert singular integral equation into a matrix equation. Convergence analysis and the stability of the proposed method is presented. Some numerical examples with comparison illustrate the efficiency of the scheme.

摘要

在文献中，很少研究无界域中奇异积分方程的数值解。本研究的主要动机是提出一种基于拉盖尔函数的实用矩阵方法来逼近积分方程的解。从拉盖尔多项式获得的拉盖尔函数用于避免大值的波动。该方案的主要特点是具有两个基函数的良好精度和较少的计算成本，这是拉盖尔函数性质及其对偶运算矩阵的结果。该矩阵等于单位矩阵，简化了逼近过程，减少了方案的计算误差。在这种技术中，双运算矩阵，采用矩阵形式和搭配方法将奇异积分方程转化为矩阵方程。收敛性分析和所提出的方法的稳定性。一些比较的数值例子说明了该方案的效率。