Taylor polynomial solutions of systems of linear differential equations with variable coefficients

A Taylor collocation method has been presented for numerically solving systems of high-order linear ordinary, differential equations with variable coefficients. Using the Taylor collocation points, this method transforms the ODE system and the given conditions to matrix equations with unknown Taylor...

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Bibliographic Details
Published in:International journal of computer mathematics 2005-06, Vol.82 (6), p.755-764
Main Authors: Sezer, Mehmet, Karamete, Ayşen, Gülsu, Mustafa
Format: Article
Language:English
Subjects:
Collocation points
System of differential equations
Taylor polynomials and series
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Summary:A Taylor collocation method has been presented for numerically solving systems of high-order linear ordinary, differential equations with variable coefficients. Using the Taylor collocation points, this method transforms the ODE system and the given conditions to matrix equations with unknown Taylor coefficients. By means of the obtained matrix equation, a new system of equations corresponding to the system of linear algebraic equations is gained. Hence by finding the Taylor coefficients, the Taylor polynomial approach is obtained. Also, the method can be used for the linear systems in the normal form. To illustrate the pertinent features of the method, examples are presented and results are compared.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160512331323336