Numerical methods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about the behavior of the solution of a suitable (basic) test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem.
A stable numerical method for Volterra Integral Equations with discontinuous kernel / Messina, Eleonora; Russo, Elvira; A., Vecchio. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 337:2(2008), pp. 1383-1393.
A stable numerical method for Volterra Integral Equations with discontinuous kernel
MESSINA, ELEONORA;RUSSO, ELVIRA;
2008
Abstract
Numerical methods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about the behavior of the solution of a suitable (basic) test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem.| File | Dimensione | Formato | |
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