Fast and precise spectral method for solving pantograph type Volterra integro-differential equations

Abstract

This paper focuses on studying a general form of pantograph type Volterra integro-differential equations (PVIDEs). We apply a new collocation spectral approach, based on shifted Chebyshev polynomials, for converting such PVIDEs into systems of algebraic equations. In addition, we apply the new spectral approach for systems of pantograph type Volterra integro-differential equations (SPVIDEs). We investigate the error analysis of the proposed numerical approach. Also, we present some comparisons with other spectral approaches for clarifying the superiority of the new spectral approach.