Open AccessPseudospectral method for semilinear partial functional differential equations
Author(s) -
Wojciech Czernous
Publication year - 2010
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2010.30.2.133
Subject(s) - mathematics , collocation (remote sensing) , convergence (economics) , boundary value problem , type (biology) , partial differential equation , mathematical analysis , stability (learning theory) , initial value problem , collocation method , differential equation , ordinary differential equation , ecology , remote sensing , machine learning , geology , computer science , economics , biology , economic growth
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