文献类型：期刊文献

英文题名：A generalized collocation method in reproducing kernel space for solving a weakly singular Fredholm integro-differential equations

作者：Zhang, Xiaoguang[1];Du, Hong[2]

机构：[1]Heilongjiang Univ Sci & Technol, Coll Sci, Harbin 150022, Heilongjiang, Peoples R China;[2]GuangDong Ocean Univ, Coll Math & Comp Sci, Zhanjiang 524000, Guangdong, Peoples R China

年份：2020

卷号：156

起止页码：158

外文期刊名：APPLIED NUMERICAL MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:000540678600011)、、EI(收录号：20203309036700)、Scopus(收录号：2-s2.0-85089189094)、WOS

基金：This work was supported by Project of Enhancing School with Innovation of GuangDong Ocean University (Grant No. Q18306), the Natural Science Foundation of Heilongjiang Province (Grant No. E2017059), Program for Scientific Research Start-up Funds of Guangdong Ocean University.

语种：英文

外文关键词：Fredholm integro-differential equation; Reproducing kernel; Weakly singular; Legendre multiwaves; Generalized collocation method

外文摘要：A generalized collocation method for solving a weakly singular Fredholm integro-differential equation with Kalman kernel is proposed in reproducing kernel space. To obtain the generalized collocation method, the multiwaves basis in reproducing kernel space Wn+1[0, b] is constructed based on Legendre multiwaves in L-2[0, 1]. Using the multiwaves basis, we propose e-approximate solutions and use the method of searching the minimum to obtain the best approximate solution of the equation. Meanwhile, convergence order and stability of the generalized collocation method are studied. It is worth to show that the generalized collocation method proposed in the paper is stable and could be applied to solve other integral equations or differential equations. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.