Symbolic and Numeric Solution of Differential Equations in Maple

Professor Keith Geddes
kogeddes@daisy.uwaterloo.ca
Symbolic Computation Group
Department of Computer Science
University of Waterloo
Waterloo, Ontario N2L 3G1
CANADA

ABSTRACT

The Maple scientific computation environment supports both symbolic and numeric mathematical computation. Techniques applied in Maple for solving ordinary differential equations (ODEs) in each of these paradigms will be surveyed. For the symbolic solution of ODEs, algorithmic methods are applied when possible. In addition, large classes of ODEs of interest in physical applications are solved by employing classification techniques which have been developed specifically for computer algebra systems. For the numeric solution of ODEs, various well-known numerical methods are available as well as some recently-developed techniques which exploit the symbolic capabilities of Maple to achieve a more powerful numerical ODE solver.