Convergence Analysis for the Chebyshev Collocation Methods to Volterra Integral Equations with a Weakly Singular Kernel  

作　　者：Xiong Liu Yanping Chen 

机构地区：[1]Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Department of Mathematics,Xiangtan University,Xiangtan,Hunan 411105,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou,Guangdong 510631,China [3]School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang,Guangdong 524048,China

出　　处：《Advances in Applied Mathematics and Mechanics》2017年第6期1506-1524,共19页应用数学与力学进展（英文）

基　　金：The authorswould like to thank the referees for the helpful suggestions.Thiswork is supported by National Science Foundation of China(Nos.91430104,11671157 and 11401347);Lingnan Normal University Project(No.2014YL1408)。

摘　　要：In this paper,a Chebyshev-collocation spectral method is developed for Volterra integral equations(VIEs)of second kind with weakly singular kernel.We first change the equation into an equivalent VIE so that the solution of the new equation possesses better regularity.The integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation points.The convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials,approximation theory for orthogonal polynomials,and the operator theory.The spectral rate of convergence for the proposed method is established in the L^(∞)-norm and weighted L^(2)-norm.Numerical results are presented to demonstrate the effectiveness of the proposed method.

关 键 词：Chebyshev collocation method Volterra integral equations spectral rate of convergence H¨older continuity 

分 类 号：O17[理学—数学]