Abstract
This paper presents a numerical method for the approximate solution of mthorder linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre series expansion approach. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple.
Highlights
Orthogonal polynomials occur often as solutions of mathematical and physical problems
Representation of a smooth function in terms of a series expansion using orthogonal polynomials is a fundamental concept in approximation theory, and forms the basis of spectral methods of solution of delay difference equations
We are concerned with the use of Laguerre polynomials to solve delay difference equations
Summary
Orthogonal polynomials occur often as solutions of mathematical and physical problems They play an important role in the study of wave mechanics, heat conduction, electromagnetic theory, quantum mechanics and mathematical statistics. They provide a natural way to solve, expand, and interpret solutions to many types of important delay difference equations. Representation of a smooth function in terms of a series expansion using orthogonal polynomials is a fundamental concept in approximation theory, and forms the basis of spectral methods of solution of delay difference equations. Based on the obtained method, we shall give sufficient approximate solution of the linear delay
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