A MODIFIED TAYLOR COLLOCATION METHOD FOR PANTOGRAPH TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH HYBRID PROPORTIONAL AND VARIABLE DELAYS

Year 2020, Volume: 6 Issue: 1, 1 - 7, 30.06.2020

Elçin Gökmen , Mehmet Sezer

https://doi.org/10.22531/muglajsci.633017

Abstract

In
this work, high order pantograph type linear functional differential equations
with hybrid proportional and variable delays is approximately solved by the
modified Taylor matrix method. With this method these functional type differential
equations are converted into the matrix form by the Taylor expansion method. The
problems are reduced into a set of algebraic equations including Taylor
coefficients. By determining the coefficients, the approximate solutions are calculated.
 Also, an error analysis technique with
residual function is developed for the presented method. Some illustrative
examples are given to demonstrate the efficiency and applicability of the
method. The computer algebraic system Maple 15 is used for all calculations and
graphs. 

Keywords

Functional differential equations, Proportional and variable delays

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