A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

作     者：CAI Hao Tao 

作者机构：School of Mathematics and Quantitative EconomicsShandong University of Finance and Economics 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第10期

页      面：2163-2178页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.10901093) National Science Foundation of Shandong Province(Grant No.ZR2013AM006) 

主　　题：second kind Fredholm integral equations with weakly singular kernels Jacobi-collocation methods stability analysis convergence analysis 

摘      要：In this work,we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular ***,we consider the case when the underlying solutions are sufficiently *** this case,the proposed method leads to a fully discrete linear *** show that the fully discrete integral operator is stable in both infinite and weighted square ***,we establish that the approximate solution arrives at an optimal convergence order under the two ***,we give some numerical examples,which confirm the theoretical prediction of the exponential rate of convergence.