The authors propose a numerical method to approximate the solution of specific bivariate Volterra integral equations which arise in the numerical solution of the initial value problem for the Korteweg-de Vries equation. A preliminary study of the domain of the unknown function is carried out and a general algorithm based on the Gauss-Legendre and Newton-Cotes quadrature formulae is developed. Numerical tests are also given in order to show the efficiency of the method.

A numerical method to compute the scattering solution for the KdV equation

Luisa Fermo;Cornelis van der Mee;Sebastiano Seatzu
2020

Abstract

The authors propose a numerical method to approximate the solution of specific bivariate Volterra integral equations which arise in the numerical solution of the initial value problem for the Korteweg-de Vries equation. A preliminary study of the domain of the unknown function is carried out and a general algorithm based on the Gauss-Legendre and Newton-Cotes quadrature formulae is developed. Numerical tests are also given in order to show the efficiency of the method.
Volterra integral equations; Korteweg-de Vries equation
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/272252
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