Volume 54, pp. 333-354, 2021.

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

Luisa Fermo and Cornelis van der Mee


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.

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Key words

Volterra integral equation, highly oscillatory kernels, Nyström method, mixed quadrature scheme, Korteweg-de Vries equation

AMS subject classifications

65R20, 41A05, 45D05.

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