Numerical methods for partial differential Volterra equations

John Whiteman

(Brunel University)

The subject of partial differential equations with memory, Volterra-type equations, is first introduced by discussing a number of physical problems which can be modelled in this way. These are mainly taken from viscoelasticity theory. The equations are essentially of canonical elliptic, parabolic and (second order) hyperbolic type, each augmented with a "hereditary" integral. The numerical analysis of problems involving these equations is briefly surveyed, after which some recent results are presented in more detail. Both classical (i.e., finite difference plus quadrature) and modern (i.e., finite element) techniques of time discretization are discussed, with particular regard in the latter case to the possibility of providing robust adaptive solvers.
Tuesday 20th February 1996, 14:30
Seminar Room 322
Department of Computer Science