基于q-Bessel多项式求柯西奇异积分方程数值解  

Numerical solutions of the Cauchy singular integral equation based on q-Bessel polynomials

作　　者：陈锐 陈冲 CHEN Rui;CHEN Chong(College of Mathematics and Information,China West Normal University,Nanchong Sichuan 637000;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637000)

机构地区：[1]西华师范的大学数学与信息学院,四川南充637000 [2]西华师范的大学公共数学学院,四川南充637000

出　　处：《宁夏师范学院学报》2023年第1期25-31,共7页Journal of Ningxia Normal University

基　　金：国家自然科学基金项目(11801456).

摘　　要：提出了基于q-Bessel多项式的离散配置法,并求解柯西奇异积分方程.首先基于q-Bessel多项式对柯西奇异积分方程中未知函数进行逼近,利用平滑变换消除积分项的奇异性.然后将积分方程转换成带有Gaussian-Legendre配置点的代数方程组,并转化成矩阵形式对其进行求解.同时给出了该方法的误差界.最后通过与文献中的其他方法进行比较,验证了该方法的可行性和有效性.The discrete collocation method based on q-Bessel polynomials is proposed to solve the Cauchy singular integral equation.Firstly,the unknown function of the Cauchy singular integral equation has been approximated by q-Bessel polynomials,and the singularity of integral term has been removed by smooth transformation.Then the system of algebraic equations with the Gauss-Legendre collocation points is reduced and solved in the matrix form.Furthermore,the error bound associated with the numerical scheme is established.Finally,double experiments display the reliability and numerical efficiency of the numerical method proposed in comparison with other schemes in reference.

关 键 词：柯西奇异积分方程 q-Bessel多项式 Gauss-Legendre求积公式 平滑变换 误差界 

分 类 号：O241.8[理学—计算数学]