Numerical Solution of Integro-Differential Equations

Abstract

In the first part of this work we take a look at the incompressible Navier Stokes equations, where the stress tensor is modeled according to the Maxwell Model for Non-Newtonian fluids. We perform a dimensional reduction of the governing equations and derive a numerical scheme for the arisng integro-differential Equations. The second part takes a look at a different integro-differential equation and we develop three different approaches for solving it. This is considered a first step for trying to solve the equations from the first part in a more general setting. The main result of this work is an algorithm that can simulate a 2D cross section of a rheometer.