Volterra integral equations with highly oscillatory kernels: A new numerical method with applications

被引：0

作者：

Fermo L. ^{[1
]}

van der Mee C. ^{[1
]}

机构：

[1] Department of Mathematics and Computer Science, University of Cagliari, Via Ospedale 72

来源：

Electronic Transactions on Numerical Analysis | 2021年 / 54卷

关键词：

Highly oscillatory kernels; Korteweg-de Vries equation; Mixed quadrature scheme; Nyström method; Volterra integral equation;

D O I：

10.1553/ETNA_VOL54S333

中图分类号：

学科分类号：

摘要：

The aim of this paper is to present a Nyström-type method for the numerical approximation of the solution of Volterra integral equations of the second kind having highly oscillatory kernels. The method is based on a mixed quadrature scheme which combines the classical product rule with a dilation quadrature formula. The convergence and the stability of the method are investigated and the accuracy of the presented approach is assessed by some numerical tests. The proposed procedure is also applied to the computation of initial scattering data related to the initial value problem associated to the Korteweg-de Vries equation. Copyright © 2021, Kent State University.

引用

页码：333 / 354

页数：21

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