SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2007-2008


Jeudi 18 octobre 2007 :  Cesar PALENCIA  (Valladolid - Espagne)
Runge-Kutta convolution quadrature methods for linear Volterra equations.

Runge-Kutta based convolution quadrature methods for abstract, well posed, linear, and homogeneous Volterra equations, non necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous one is given. The error and stability analysis is based on this representation, which also shows that the numerical solution inherits some interesting qualitative properties, such as positivity, of the exact solution. Numerical illustrations are provided.