Abstract
This study presents a new method for the solution of mth-order linear differential-difference equations with variable coefficients under the mixed conditions. We introduce a Fibonacci collocation method based on the Fibonacci polynomials for the approximate solution. Numerical examples are included to demonstrate the applicability of the technique. The obtained results are compared by the known results.
Highlights
IntroductionThe study of the differential-difference equations developed very rapidly in recent years [1,2,3]
The study of the differential-difference equations developed very rapidly in recent years [1,2,3]. These equations play an important role in various branches of science such as engineering, mechanics, physics, biology, control theory etc
A considerable advantage of this method is that Fibonacci coefficients of the solution are obtained very by using the computer programs
Summary
The study of the differential-difference equations developed very rapidly in recent years [1,2,3]. These equations play an important role in various branches of science such as engineering, mechanics, physics, biology, control theory etc. Approximate solutions of linear differential, difference, differential-difference, integral and integro-differentialdifference, pantograph equations have been found using the Taylor collocation method and Chebyshev polynomial method by Sezer et al [8,9,10,11,12,13,14]. The Fibonacci matrix method has been used to find the approximate solutions of differential and integrodifferential equations [15]
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