Pseudospectral method for semilinear partial functional differential equations

Abstract

We present a convergence result for two spectral methods applied to an initial boundary value problem with functional dependence of Volterra type. Explicit condition of Courant-Friedrichs-Levy type is assumed on time step τ and the number $N$ of collocation points. Stability statements and error estimates are written using continuous norms in weighted Jacobi spaces.