Guide expansions for the recursive parametric solution of polynomial dynamical systems

ANZIAM J. 47 (2006), 387-396

Guide expansions for the recursive parametric solution of polynomial dynamical systems

G. F. D. Duff
deceased
formerly of the Department of Mathematics
University of Toronto

R. B. Leipnik
Mathematics Department
University of California
Santa Barbara
CA 93106--3080
USA
leipnik@math.ucsb.edu

and

C. E. M. Pearce
School of Mathematical Sciences
The University of Adelaide
Adelaide SA 5005
Australia
charles.pearce@adelaide.edu.au

Abstract

Recursive parametric series solutions are developed for polynomial ODE systems, based on expanding the system components in series of a form studied by Weiss. Individual terms involve first-order driven linear ODE systems with variable coefficients. We consider Lotka-Volterra systems as an example.

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