Opuscula Math. 30, no. 2 (2010), 133-145

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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  • Wojciech Czernous
  • University of Gdansk, Institute of Mathematics, ul. Wita Stwosza 57, 80-952 Gdansk, Poland
  • Received: 2009-12-03.
  • Revised: 2010-01-12.
  • Accepted: 2010-01-18.
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Cite this article as:
Wojciech Czernous, Pseudospectral method for semilinear partial functional differential equations, Opuscula Math. 30, no. 2 (2010), 133-145, http://dx.doi.org/10.7494/OpMath.2010.30.2.133

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