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

作　　者：CAI Hao Tao 

机构地区：[1]School of Mathematics and Quantitative Economics,Shandong University of Finance and Economics

出　　处：《Science China Mathematics》2014年第10期2163-2178,共16页中国科学：数学（英文版）

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

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

关 键 词：second kind Fredholm integral equations with weakly singular kernels Jacobi-collocation methods stability analysis convergence analysis 

分 类 号：O175.5[理学—数学] O241.8[理学—基础数学]