A Spectral Method for Pantograph-Type Delay Differential Equations and Its Convergence Analysis (Journal of Computational Mathematics, 2018)
We propose a novel numerical approach for delay differential equations with vanishingproportional delays based on spectral methods. A Legendre-collocation method is employedto obtain highly accurate numerical approximations to the exact solution. It isproved theoretically and demonstrated numerically that the proposed method convergesexponentially provided that the data in the given pantograph delay differential equationare smooth.