Opuscula Math. 30, no. 2 (2010), 133-145
http://dx.doi.org/10.7494/OpMath.2010.30.2.133

Opuscula Mathematica

# Pseudospectral method for semilinear partial functional differential equations

Wojciech Czernous

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.

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