Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations

In this paper, a spectral collocation method for solving nonlinear pantograph type delay differential equations is presented. The basis functions used for the spectral analysis are based on Chebyshev, Legendre, and Jacobi polynomials. By using the collocation points and operations matrices of required functions such as derivative functions and delays of unknown functions, the method transforms the problem into a system of nonlinear algebraic equations. The solutions of this nonlinear system determine the coefficients of the assumed solution. The method is explained by numerical examples and the results are compared with the available methods in the literature. It is seen from the applications that our method gives more efficient results than that of the reported methods.