Taylor collocation method for systems of high-order linear differential–difference equations with variable coefficients | Zendy

Elçin Gökmen | Zendy; Mehmet Sezer | Zendy

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Taylor collocation method for systems of high-order linear differential–difference equations with variable coefficients

Author(s) -

Elçin Gökmen,

Mehmet Sezer

Publication year - 2012

Publication title -

ain shams engineering journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.505

H-Index - 46

eISSN - 2090-4495

pISSN - 2090-4479

DOI - 10.1016/j.asej.2012.07.005

Subject(s) - taylor series , mathematics , orthogonal collocation , collocation method , collocation (remote sensing) , taylor's theorem , algebraic equation , coefficient matrix , mathematical analysis , differential equation , polynomial , matrix (chemical analysis) , divided differences , nonlinear system , ordinary differential equation , computer science , physics , eigenvalues and eigenvectors , materials science , machine learning , quantum mechanics , composite material

A Taylor collocation method has been developed to solve the systems of high-order linear differential–difference equations in terms of the Taylor polynomials. Using the Taylor collocation points, this method transforms differential–difference equation systems 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 easily, Taylor polynomial solutions are obtained. To illustrate the pertinent features examples are presented and results are compared. All numerical computations have been performed on the computer algebraic system Maple 9

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