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.