A NUMERICAL APPROACH FOR SOLVING PANTOGRAPH-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MIXED DELAYS USING DICKSON POLYNOMIALS OF THE SECOND KIND

Abstract

In this study, a hybrid matrix-collocation method based on Dickson polynomials of the second kind along with Taylor polynomials is proposed to solve pantograph type functional differential equations with mixed delays under the initial conditions. The parameter-alpha in Dickson polynomials is interpreted for obtaining the optimum solutions. An error estimation related with the residual function and the mean-value theorem is implemented and also some illustrative examples are presented. It is observed that the proposed method is easy to be applied.