The automatic solution of systems of ordinary differential equations by the method of Taylor series

Abstract

The paper presents a simple langauge for the specification of mixedalgebraic-ordinary differential systems with initial conditions.The language is specified in a BNF-type form. It is shown how tocompile and optimise this language. The authors then apply the automaticdifferentiation technique of [Moore1966IA] to generate the Taylorseries solution of a system specified in this language. Some simpleexamples of the language are given, but no numerical results areprovided.