第一类柯西奇异积分方程的有效配置求解法  

The Efficient Collocation Method for Solving the First Kind of Cauchy Singular Integral Equation

作　　者：陈锐 陈冲 

机构地区：[1]西华师范大学数学与信息学院,四川 南充 [2]西华师范大学公共数学学院,四川 南充

出　　处：《理论数学》2023年第4期968-975,共8页Pure Mathematics

摘　　要：本文提出了求解第一类柯西奇异积分方程的一种有效配置法,即基于q-Bessel多项式并结合第一类、第二类高斯–切比雪夫求积公式的离散配置法将第一类柯西奇异积分方程转化为线性方程组进行近似求解,结合插值理论对该方法进行误差分析。通过数值算例验证了该方法的可行性和有效性。This paper presents an efficient collocation method to solve Cauchy singular integral equations of the first kind. Namely, based on the q-Bessel polynomial and the discrete collocation method of the first and second Gauss-Chebyshev quadrature formulas, the first Cauchy singular integral equation is transformed into a linear system of equations for approximate solution, and the error analysis of the method is carried out by combining the interpolation theory. The effectiveness and feasibility of the method are verified by numerical examples.

关 键 词：柯西奇异积分方程 q-Bessel多项式 高斯–切比雪夫求积公式 误差分析 

分 类 号：G63[文化科学—教育学]