On the convergence of difference schemes for hyperbolic problems with concentrated data

SIAM Journal on Numerical Analysis

Volumn 41, Issue 2, 2003, Pages 516-538

  Jovanović, Bosko S ^a   Vulkov, Lubtn G ^b  

^a UNIVERSITY OF BELGRADE   (Serbia)

^b UNIVERSITY OF RUSE   (Bulgaria)

Author keywords

Concentrated mass; Difference scheme; Generalized solution; Rate of convergence; Sobolev spaces

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; DATA REDUCTION; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; ESTIMATION;

CONCENTRATED MASS; DIFFERENCE SCHEMES; GENERALIZED SOLUTION; RATE OF CONVERGENCE; SOBOLEV SPACES;

PROBLEM SOLVING;

EID: 2342570950     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900382983     Document Type: Article

References (22)

1. I. BRAIANOV, Convergence of a Crank-Nicolson difference scheme for heat equation with interface in the heat flow and concentrated heat capacity, Lecture Notes in Comput. Sci., 1196 (1997), pp. 58-65.
2. I. BRAIANOV AND L. VULKOV, Finite difference schemes with variable weights for parabolic equations with concentrated capacity, Notes Numer, Fluid Dynam. 62, Vieweg, Braun-schweig, Germany, 1998, pp. 208-216.
3. I. A. BRAIANOV AND L. G. VULKOV, Homogeneous difference schemes for the heat equation with concentrated capacity, Comput. Math. Math. Phys., 39 (1999), pp. 254-261 (in Russian).
4. B. S. JOVANOVIĆ, Finite difference method for boundary value problems with weak solutions, Technical report, Posebna izdanja Mat. Instituta 16, Belgrade, Yugoslavia, 1993.
5. B. S. JOVANOVIĆ, Convergence of a finite-difference scheme for hyperbolic equations with variable coefficients, Z. Angew. Math. Mech., 72 (1992), pp. 493-496.
6. B. S. JOVANOVIĆ, L. D. IVANOVIĆ, AND E. E. SÜLI, Convergence of a finite difference scheme for second-order hyperbolic equations with variable coefficients, IMA J. Numer. Anal., 7 (1987), pp. 39-45.
7. B. S. JOVANOVIĆ. J. D. KANDILAROV, AND L. G. VULKOV, Construction and convergence of a difference scheme for a model elliptic equation with Dirac-delta function coefficient, Lecture Notes in Comput. Sci., 1988 (2001), pp. 431-438.
8. B. S. JOVANOVIĆ, P. P. MAT-US, AND V. S. SHCHEGLIK, Convergence rate estimates for parabolic problems with variable coefficients and generalized solutions, Sib. Zh. Vychisl. Mat., 2 (1999), pp. 123-136 (in Russian).
9. B. JOVANOVIĆ AND L. VULKOV, On the convergence of finite difference schemes for the heat equation with concentrated capacity, Numer. Math., 89 (2001), pp. 715-734.
10. B. S. JOVANOVIĆ AND L. G. VULKOV, Operator's approach to the problems with concentrated factors, Lecture Notes in Comput. Sci., 1988 (2001), pp. 439-450.
11. B. S. JOVANOVIĆ AND L. G. VULKOV, On the convergence of difference schemes for the string equation with concentrated mass, ' in Proceedings of the 4th International Conference on Finite-Difference Schemes: Theory and Applications, R. Ciegis, A. Samarskǐ, and M. Sapagovas, eds., IMI, Vilnius, Lithuania, 2000, pp. 107-116.
12. R. D. LAZAROV, V. L. MAKAROV, AND A. A. SAMARSKIǐ, Applications of exact difference scheme for construction and studies of difference schemes on generalized solutions, Math. Sbornik, 117 (1982), pp. 469-480 (in Russian).
13. J. L. LIONS AND E. MAGENES, Non Homogeneous Boundary Value Problems and Applications, Springer-Verlag, Berlin, New York, 1972.
14. L. A. OGANESYAN AND L. A. RUKHOVETS, Variational-Difference Methods for Solution of Elliptic Equations, AS Arm., Erevan, Armenia, 1979 (in Russian).
15. F. RIESZ AND B. SZ.-NAGY, Leçons d'analyse fonctionelle, Akadémiai Kiadó, Budapest, 1972.
16. A. A. SAMARSKIǏ, Theory of Difference Schemes, Nauka, Moscow, 1989 (in Russian).
17. A. A. SAMARSKIǏ, R. D. LAZAROV, AND V. L. MAKAROV, Difference Schemes for Differential Equations with Generalized Solutions, Vyshaya Shkola, Moscow, 1987 (in Russian).
18. A. A. SAMARSKIǏ, V. I. MAZHUKIN, D. A. MALAFEǏ, AND P. P. MATUS, Difference schemes of high order of approximation on non uniform in space meshes, Dokl. RAN (Russian Academy of Sciences), 36 (1999), pp. 1-4 (in Russian).
19. A. N. TIKHONOV AND A. A. SAMARSKIǏ, Equations of Mathematical Physics, GITTL, Moscow, 1953 (in Russian).
20. V. S. VLADIMIROV, Equations of Mathematical Physics, Nauka, Moscow, 1988 (in Russian).
21. L. VULKOV, Application of Steklov-type eigenvalues problems to convergence of difference schemes for parabolic and hyperbolic equations with dynamical boundary conditions, Lecture Notes in Comput. Sci., 1196 (1997), pp. 557-564.
22. J. WLOKA, Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1987.