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

Electronic Transactions on Numerical Analysis

article

Luisa Fermo¹  Cornelis van der Mee¹ 

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

关键词: Volterra integral equation;    highly oscillatory kernels;    Nyström method;    mixed quadrature scheme;    Korteweg-de Vries equation;   

DOI  :  10.1553/etna_vol54s333

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 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.

【 授权许可】

Unknown