A Numerical algorithm with residual error estimation for solution of high-order Pantograph-type functional differential equations using Fibonacci polynomials

In this article a functional differential equation known as the high-order delay pantograph-type equation, which contains a linear functional argument, is considered and a new matrix method based on the Fibonacci polynomials and collocation points is presented to find the approximate solution of the pantograph equations under the initial conditions. Also, the numerical examples are given demonstrate the applicability of the technique. In addition, an error analysis technique based on residual function is developed and applied to some problems to demonstrate the validity of the method.