文献类型：期刊文献

英文题名：A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel

作者：Du, Hong[1];Chen, Zhong[2];Yang, Tiejun[3]

机构：[1]GuangDong Ocean Univ, Coll Math & Comp Sci, ZhanJiang 524000, Guangdong, Peoples R China;[2]Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Shandong, Peoples R China;[3]GuangDong Ocean Univ, Div Sci & Technol, ZhanJiang 524000, Guangdong, Peoples R China

年份：2020

卷号：157

起止页码：210

外文期刊名：APPLIED NUMERICAL MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:000564648400011)、、EI(收录号：20202608865705)、Scopus(收录号：2-s2.0-85086714755)、WOS

基金：This work was supported by GuangDong Ocean University (Grant No. Q18306, R20050), the NSF of Heilongjiang Province (Grant No. E2017059).

语种：英文

外文关键词：Fractional integro-differential equation; Least residue method; Reproducing kernel; Legendre wavelets; Weakly singular

外文摘要：A stable least residue method for solving a nonlinear fractional integro-differential equation with a weakly singular kernel in the reproducing kernel space is proposed. To solve the equation, the multiwavelets bases in the reproducing kernel space are constructed based on the cubic Legendre wavelets in L-2[0, 1]. The best approximate solution could be obtained by solving the normal equation. Meanwhile, we provide the adaptive convergence order and the stability proof of the scheme. It is encouraging that the new method is stable and the accuracy of the method is preserved even in the case if the solution has fast oscillations. Four examples strongly demonstrate the validity of the scheme. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.