文献类型：期刊文献

英文题名：A new reproducing kernel method for Duffing equations

作者：Chen, Zhong[1];Jiang, Wei[1];Du, Hong[2]

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

年份：2021

卷号：98

期号：11

起止页码：2341

外文期刊名：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:000628226000001)、、EI(收录号：20211210098550)、Scopus(收录号：2-s2.0-85102588267)、WOS

基金：This work has received various grants from National Natural Science Foundation of China [grant number 11701124], Natural Science Foundation of Heilongjiang Province [grant number E2017059], Project of Enhancing School with Innovation [grant number Q18306] and Scientific Research Start-up Funds (No.R20050) of GuangDong Ocean University.

语种：英文

外文关键词：Duffing equation; reproducing kernel; spline function; convergence order; Newton iterations

外文摘要：Reproducing kernel theories have attracted much attention for solving various problems. However, discussions of stability and convergence order are very difficult in the traditional reproducing kernel method by orthogonal expansion because of the randomness of Schmidt's orthogonalization coefficients. Later, the convergence order of the reproducing kernel method is estimated by polynomial interpolation of residuals. But the convergence order is not high. In this paper, taking Duffing equation as an example, noting that the reproducing kernel function is a spline function, a new scheme with much higher convergence order is proposed by constructing spline bases function in the reproducing kernel space and combining polynomial interpolation of residuals. Numerical examples verify the convergence order theories proposed in this paper. It is worth to say that our main results could be applied to construct approximate solutions of various equations.