Solving systems of high-order linear differential–difference equations via Euler matrix method | Zendy

Farshid Mirzaee | Zendy; Saeed Bimesl | Zendy

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Solving systems of high-order linear differential–difference equations via Euler matrix method

Author(s) -

Farshid Mirzaee,

Saeed Bimesl

Publication year - 2014

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.1016/j.joems.2014.05.003

Subject(s) - mathematics , coefficient matrix , matrix (chemical analysis) , euler method , euler's formula , algebraic equation , differential equation , backward euler method , basis (linear algebra) , matrix difference equation , mathematical analysis , euler equations , nonlinear system , riccati equation , geometry , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , composite material

This paper contributes a new matrix method for solving systems of high-order linear differential–difference equations with variable coefficients under given initial conditions. On the basis of the presented approach, the matrix forms of the Euler polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Euler coefficients are determined. Some illustrative examples with comparisons are given. The results demonstrate reliability and efficiency of the proposed method

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