A power series method for solving initial value problems utilizing computer algebra systems

Abstract

This paper introduces an iterative method for generating the Taylor polynomial of the solution to an analytic initial value problem and is based upon the utilisation of a symbolic manipulation language. As developed here, the mth iterate of this procedure is precisely the mth degree Taylor polynomial of the solution. Error estimates are provided which are readily calculated with a computer algebra system. Examples are presented which illustrate the method and its ease of application.

Keywords:

• Initial value problems
• symbolic manipulation

C.R.Cateories:

• G.1.5
• G.1.7
• I.1.2
• I.1.4

¹Research supported by the Texas Advanced Research Program, under Grant No. 003644-101

¹Research supported by the Texas Advanced Research Program, under Grant No. 003644-101

Notes

¹Research supported by the Texas Advanced Research Program, under Grant No. 003644-101