Numerical Solutions of Delay Differential Equations Using Spectral Methods

In this talk I shall present an efficient numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. We develop a spectral approach for the pantograph type-delay differential equations. A Legendre spectral-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. The exponential convergence was obtained theoretically which was confirmed by some numerical examples, provided the data in the given pantograph delay differential equation are smooth. We also discuss briefly the case of nonlinear and system of pantograph-type delay
differential equations.