On the convergence of finite difference schemes for the heat equation with concentrated capacity

Numerische Mathematik

Volumn 89, Issue 4, 2001, Pages 715-734

  Jovanovic, B S ^a   Vulkov, L G ^b  

^a UNIVERSITY OF BELGRADE   (Serbia)

^b UNIVERSITY OF RUSE   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035623410     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100280     Document Type: Article

References (16)

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2. Braianov, I.A.; Vulkov, L.G.: Homogeneous difference schemes for the heat equation with concentrated capacity. Zh. Vychisl. Math. Math. Phys. 39 (1999), pp. 254-261 (Russian)
3. Braianov, I.; Vulkov, L.: Finite Difference Schemes with Variable Weights for Parabolic Equations with Concentrated Capacity. Notes on Numerical Fluid Dynamics, Vieweg, Vol. 62 (1998), pp. 208-216
4. Elshner, J.: Quasilinear parabolic systems with dynamical boundary conditions. Communs Part. Diff. Eqtns. 19 (1993), pp. 1309-1364
5. Goolin A. V: Stability of symetrizable difference schemes. In: Finite Difference Methods: Theory and Applications, edited by A.A. Samarskii, P.N. Vabishchevich, L.G. Vulkov. New York: Nova Science (1998), pp. 95-102
6. Jovanovic, B.S.: Finite difference method for boundary value problems with weak solutions. Posebna izdanja Mat. Instituta 16, Belgrade 1993
7. Jovanovic, B.S.; Matus, P.P.; Shcheglik, V.S.: Difference schemes on nonuniform meshes for parabolic equations with variables coefficients and generalized solutions. DNAN Belarus 42(6) (1998), 38-44 (Russian)
8. Lazarov, R.D.; Makarov, V.L.; Samarskii, A.A.: Applications of exact difference schemes for construction and studies of difference schemes on generalized solutions. Math. Sbornik 117 (1982), 469-480 (Russian)
9. Lions, J.L.; Magenes, E.: Non homogeneous boundary value problems and applications. Berlin, New York: Springer, 1972
10. Lykov, A.V.: Heat and mass transfer. Spravochnik. Moscow: Nauka, 1989 (Russian)
11. Renardy, M., Rogers, R. C.: An introduction to partial differential equations. Berlin, New York: Springer, 1993
12. Samarskii, A.A.: Theory of difference schemes. Moscow: Nauka, 1989 (Russian)
13. Samarskii, A.A.; Lazarov, R.D.; Makarov, V.L.: Difference schemes for differential equations with generalized solutions. Moscow: Vysshaya Shkola, 1987 (Russian)
14. Vladimirov, V.S.: Equations of the mathematical physics. Moscow: Nauka, 1988 (Russian)
15. Vulkov, L: Applications of Steklov-type eigenvalues problems to convergence of difference schemes for parabolic and hyperbolic equations with dynamical boundary conditions. Lect. Notes Comput. Sci. Vol. 1196 (1997), pp. 1309-1364. Berlin, Heidelberg, New York: Springer
16. Wloka, J.: Partial differential equations. Cambridge: Cambridge University Press, 1987