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 \(\tau \) and the number \(N\) of collocation points. Stability statements and error estimates are written using continuous norms in weighted Jacobi spaces.
Keywords: pseudospectral collocation, CFS condition, convergence, error estimates.
Mathematics Subject Classification: 65M70, 35R10.