An explicit method for solving flows of ODE

Abstract

This paper is concerned with finding numerical solutions of a flow of ODE solutions. It describes a new method for finding solutions of problems, when the flow field is not given explicitly, using an implicit method, in particular Euler Backward, as well as interpolation. The special aspect is that the method as such is explicit, and resolves the flow with a similar accuracy as Euler Backward, even when the problem is stiff. An analysis is given of both stability and accuracy and extensions to non-autonomous problems are discussed. A number of numerical examples illustrates this analysis.