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1993•International Journal of Computer MathematicsRequires access

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

Lawrence Schovanec, John T. White

Open publisher page 5 citations

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.

About this research paper

What this paper is about

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.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Symbolic computation, Power series, Taylor series, Polynomial, Mathematics, Algebra over a field, Series (stratigraphy), Iterative method

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