A note on the second order of accuracy difference schemes for hyperbolic-parabolic equations

Applied Mathematics and Computation

Volumn 165, Issue 3, 2005, Pages 517-537

  Ashyralyev, A ^a,b   Yurtsever, H A ^a  

^a FATIH UNIVERSITY   (Turkey)

^b Intl Turkmen Turkish University   (Turkmenistan)

Author keywords

Difference schemes; Hyperbolic parabolic equation; Stability

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFERENCE EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

ACCURACY DIFFERENCE SCHEMES; DIFFERENCE SCHEMES; HILBERT SPACE; HYPERBOLIC-PARABOLIC EQUATIONS; STABILITY ESTIMATES;

BOUNDARY VALUE PROBLEMS;

EID: 18144388326     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.04.033     Document Type: Article

References (29)

1. M.S. Salahatdinov Equations of Mixed-Composite Type 1974 FAN Tashkent (Russian) [RZh. Mat. 1974:7 B380 K]
2. T.D. Djuraev Boundary Value Problems for Equations of Mixed and Mixed-Composite Types 1978 FAN Tashkent (Russian) [RZh. Mat. 1979:12 B380 K]
3. D. Bazarov, and H. Soltanov Some Local and Nonlocal Boundary Value Problems for Equations of Mixed and Mixed-Composite Types 1995 Ilim Ashgabat (Russian)
4. A. Ashyralyev, and A. Yurtsever On a nonlocal boundary value problem for hyperbolic-parabolic equations Application of Mathematics in Engineering and Economics vol. 26 2001 Heron Press and Technical University of Sofia pp. 79-85
5. A. Ashyralyev, and A. Yurtsever On a nonlocal boundary value problem for semilinear hyperbolic-parabolic equations Nonlin. Anal., Theory, Methods Appl. 47 2001 3585 3592
6. A. Ashyralyev, and A. Yurtsever On difference schemes for hyperbolic-parabolic equations Funct. Diff. Equat. 7 3-4 2000 189 203
7. S.G. Krein, Linear Differential Equations in Banach space, Nauka, Moscow, 1966 (Russian) [MR 40 # 508];
8. English transl.: Linear Differential Equations in Banach space, Translations of Mathematical Monographs, vol. 23, American Mathematical Society, Providence, RI, 1968 [MR 39 #3159b]
9. A. Ashyralyev, I. Muradov, On hyperbolic-parabolic equations in a Hilbert space, in: Problems of Mathematics and of Economical Models of Turkmenistan, Ashgabat, 1995, pp. 26-28 (Russian)
10. A. Ashyralyev, The stability of difference schemes for partial differential equations of mixed types, in: Proceedings of the Second International Symposium on Mathematical and Computational Applications, Baku, 1999, pp. 314-316
11. A. Ashyralyev, H. Akca, and L. Biszewski On a semilinear evolution nonlocal Cauchy problem Some Problems of Applied Mathematics 2000 Fatih University Istanbul 29 44
12. A. Ashyralyev, and P.E. Sobolevskii Well-Posedness of Parabolic Difference Equations 1994 Birkhäuser Verlag Basel [MR 95J:65094]
13. A. Samarskii, and V. Andr'eev M'ethodes aux diff'erences pour'equations elliptiques 1978 Editions Mir Moscow
14. A. Ashyralyev, and I. Karatay On the second order of accuracy difference schemes of the nonlocal boundary value problem for parabolic equations Funct. Diff. Equat. 10 1-2 2003 45 63
15. h of one-dimensional difference operators with nonlocal boundary conditions Some Problems of Applied Mathematics 2000 Fatih University Istanbul 56 70
16. A. Ashyralyev Estimation of the convergence for the solution of the modified Crank-Nicolson difference schemes for the parabolic equations with the nonsmooth initial data IZV. Akad. Nauk Turkmen. SSR Ser. Fiz.-Tekhn. Khim. Geol. Nauk 1 1989 3 8 (Russian)
17. A. Samarskii, and A.V. Gulin Stability of Difference Schemes 1973 Nauka Moscow (Russian)
18. R. Rannacher Discretization of the heat equation with singular initial data Z. Angew. Math. Mech. 62 5 1982 346 348
19. A. Ashyralyev, and P.E. Sobolevskii A note on the difference schemes for hyperbolic equations Abstr. Appl. Anal. 6 2 2001 63 70
20. A. Ashyralyev, N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations. in: Proceeding of the International Conference "Modern problems of Functional Analysis and Differential Equations", Voronezh, June 30-July 4, 2003, pp. 21-22
21. A. Ashyralyev, and P.E. Sobolevskii Well-posed solvability of the Cauchy problem for the difference equations of the parabolic type Nonlin. Anal., Theory, Methods Appl. 24 2 1995 257 264
22. A. Ashyralyev, and P.E. Sobolevskii Difference schemes of a high order of accuracy for parabolic equations with the variable coefficients Dokl. Akad. Nauk Ukrainian SSR, Ser. À Fiz. - Math. and Tech. Sci. 6 1988 3 7 (Russian)
23. p([0, 1],E) spaces Numer. Funct. Anal. Optim. 23 7-8 2002 669 693
24. M. Crouzeix, S. Larson, S. Piskarev, and V. Thomée The stability of rational approximations of analytic semigroups BIT 33 1 1993 74 84
25. I.P. Gavrilyuk, V.L. Makarov, Exponentially convergent parallel disretization methods for the first order evolution equations, Preprint Institut für Angewandte Analysis und Stochastik (WIAS), Berlin, 2000, p. 28
26. I.P. Gavrilyuk Strongly p-positive operators and explicit representations of the solutions of initial value problems for second-order differential equations in Banach space J. Math. Anal. Appl. 236 2 1999 327 349 [MR 2001i:34072]
27. Y.G. Wang, and M. Oberguggenberger Nonlinear parabolic equations with regularized derivatives J. Math. Anal. Appl. 233 2 1999 644 658
28. W.-J. Beyn, and B.M. Garay Estimates of variable stepsize Runge Kutta methods for sectorial evolution equations with nonsmooth data Appl. Numer. Math. 41 3 2002 369 400
29. 2,r-convergent approximation schemes to the Navier-Stokes equations Nonlin. Anal., Theory, Methods Appl. 30 4 1997 1915 1926