Exponentially convergent parallel discretization methods for the first order evolution equations

Computational Methods in Applied Mathematics

Volumn 1, Issue 4, 2001, Pages 333-355

  Gavrilyuk, Ivan P ^a   Makarov, Vladimir L ^b  

^a Staatliche Studienakademie Am Wartenberg 2   (Germany)

^b INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

Evolution equations; Quadrature rule; Strongly P positive operators; Unbounded operator coefficients

Indexed keywords

EID: 85009773228     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2001-0022     Document Type: Article

References (15)

1. Schwarz methods for obstacle problems with convection-diffusion operators, in: Handbook of Numerical Analysis (P. Ciarlet and J. Lions, eds.), vol. 1, North-Holland, Amsterdam, 1990, pp. 251-256.
2. S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Commuications on Pure and Applied Mathematics, XV (1962), pp. 119-147.
3. A. Ashyralyev and P. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Birkhäuser Verlag, 1994.
4. H. Bateman and A. Erdelyi, Higher Transcendental Functions, Mc Graw-Hill Book Company, Inc., 1953.
5. C. Bernardi and Y. Maday, Approximations Spectrales de Problemes aux Limites Elliptiques, SpringerVerlag, 1992.
6. T. Carleman, Uber die asymptotische Verteilung der eigenwerte partieller differentialgleichungen, Ber. der Sächs. Akad Wiss. Leipzig, Math.-Nat.Kl., 88 (1936), pp. 119-132.
7. I. Gavrilyuk, Strongly p-positive operators and explicit representation of the solutions of initial value problems for second order differential equations in banach space, Journ. of Math. Analysis and Appl., 236 (1999), pp. 327-349.
8. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, Clarendon Press, New York, Oxford, 1985.
9. S. Krein, Linear Differential Operators in Banach Spaces, TAMS, New York, 29, 1971.
10. R. Kress, Linear Integral Equations, Springer-Verlag, Berlin et al., 1989.
11. A. Pazy, Semigroups of Linear Operators and Applications to Partial Difference Equations, SpringerVerlag, Berlin et al, 1983.
12. D. Sheen, I. Sloan, and V. Thomeé, A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature, Mathematics of Computation, 69, pp. 177-195.
13. F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer-Verlag, Beijing, 1993.
14. G. Szegä, Orthogonal Polynomials, AMS, New York, 1959.
15. V. Thomeé, Finite difference methods for linear parabolic equations, in: Handbook of Numerical Analysis, vol. 1, North-Holland, Amsterdam, 1990, pp. 251-256.