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Języki publikacji
Abstrakty
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
133--145
Opis fizyczny
Bibliogr. 8 poz., tab.
Twórcy
autor
- University of Gdańsk Institute of Mathematics ul. Wita Stwosza 57, 80-952 Gdańsk, Poland, czernous@mat.ug.edu.pl
Bibliografia
- [1] R.A. Adams, J.F. Fournier, Sobolev Spaces, 2nd ed., Pure and Applied Mathematics 140, Academic Press, Elsevier Science, 2003.
- [2] C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral methods in fluid dynamics, Springer-Verlag, New York, 1988.
- [3] D. Gottlieb, L. Lustman, E. Tadmor, Stability analysis of spectral methods for hyperbolic initial-boundary value systems, SIAM J. Numer. Math. 24 (1987), 241–256.
- [4] D. Gottlieb, E. Tadmor, The CFL condition for spectral approximations to hyperbolic initial-boundary value problems, Mathematics of Computation 56 (1991) 194, 565–588.
- [5] Ben-Yu Guo, Wang Li-Lian, Jacobi interpolation approximations and their applications to singular differential equations, Adv. Comput. Math. 14 (2001), 227–276.
- [6] Ben-Yu Guo, Wang Li-Lian, Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces, Journal of Approximation Theory 128 (2004), 1–41.
- [7] Z. Kamont, Hyperbolic functional differential inequalities and applications, Mathematics and its Applications, 486, Kluwer Academic Publishers, Dordrecht, 1999.
- [8] G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Soc., New York, 1975.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0002-0019