A Taylor polynomial approach for solving differential-difference equations

Authors:
Mustafa Gülsu;Mehmet Sezer
Affiliations:
Department of Mathematics, Faculty of Science, Mugla University, Mugla, Turkey;Department of Mathematics, Faculty of Science, Mugla University, Mugla, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
Cited 3

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Numerical solution of the higher-order linear Fredholm integro-differential-difference equation with variable coefficients

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Abstract

The purpose of this study is to give a Taylor polynomial approximation for the solution of mth-order linear differential-difference equations with variable coefficients under the mixed conditions about any point. For this purpose, Taylor matrix method is introduced. This method is based on first taking the truncated Taylor expansions of the functions in the differential-difference equations and then substituting their matrix forms into the equation. Hence, the result matrix equation can be solved and the unknown Taylor coefficients can be found approximately. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed. Also we have discussed the accuracy of the method. We use the symbolic algebra program, Maple, to prove our results.