Explicitly solving vectorial ODEs

Abstract

This paper concerns a new method for finding numerical solutions of multivariate ODE flows, where the flow field is not given explicitly. The method is based on the existing implicit numerical methods, such as Euler Backward and the implicit midpoint rule. The main aspect is that the method as such is explicit, but with the similar accuracy and stability properties as the original (implicit) methods. A higher dimensional analysis is given of both stability and accuracy. A couple of examples illustrates this analysis.

Numerical modelling of the blowing phase in the production of glass containers

“…A third option to perform time integration is the so called flow method developed in [14]. Time integration is explicit in this method and only one Stokes problem needs to be solved at each time step, while accuracy is second order.…”