论文标题
使用Jacobi小波的一类第三种Volterra积分方程的数值解
Numerical solution of a class of third-kind Volterra integral equations using Jacobi wavelets
论文作者
论文摘要
我们提出了一种基于广义的雅各比小波以及高斯 - 雅各比正方形公式的光谱搭配方法，用于求解一类第三种伏尔泰拉积分方程。为此，通过考虑合适的变量更改，首先将积分间隔转换为间隔[-1,1]。然后，通过引入特殊的Jacobi参数，使用高斯 - 雅各比二次规则近似整体零件。根据未知系数的雅各比小波函数，考虑了未知函数的近似值，必须确定。通过将此近似值代替到方程中，并在一组搭配点处将所得方程式置，可以获得线性代数方程系统。然后，我们建议一种确定达到一定精度所需的基础功能数量的方法。最后，包括一些示例，以说明新方案的适用性，效率和准确性。
We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss-Jacobi quadrature formula, for solving a class of third-kind Volterra integral equations. To do this, the interval of integration is first transformed into the interval [-1,1], by considering a suitable change of variable. Then, by introducing special Jacobi parameters, the integral part is approximated using the Gauss-Jacobi quadrature rule. An approximation of the unknown function is considered in terms of Jacobi wavelets functions with unknown coefficients, which must be determined. By substituting this approximation into the equation, and collocating the resulting equation at a set of collocation points, a system of linear algebraic equations is obtained. Then, we suggest a method to determine the number of basis functions necessary to attain a certain precision. Finally, some examples are included to illustrate the applicability, efficiency, and accuracy of the new scheme.
