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

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.