A Third Order Method for Convection-Diffusion Equations with a Delay Term

The numerical solution of a parabolic convection diffusion equation with delay term is considered. This includes both variants, the initial value problem and the prehistory problem. Equations with a delay or memory term, often called integrodifferential problems, appear in different contexts of heat conduction in materials with memory, viscoelasticity and population models. This work concentrates on the linear convection diffusion case of the prehistory and the initial value problem. One problem concerning delay or memory problems is the data storage. To deal with this problem an adaptivity method of third order in time is developed to save storage data at smooth parts of the solution. Numerical results for higher Peclet numbers are presented.