A Taylor polynomial approach for solving differential-difference equations
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摘要
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.
论文关键词:39A10,41A10,65Q05,Taylor polynomials and series,Taylor polynomial solutions,Taylor matrix method,Differential-difference equations
论文评审过程:Received 29 June 2004, Revised 17 February 2005, Available online 7 April 2005.
论文官网地址:https://doi.org/10.1016/j.cam.2005.02.009