Difference schemes with nonlocal boundary conditions

Computational Methods in Applied Mathematics

Volumn 1, Issue 1, 2001, Pages 62-71

  Goolin, Alexei V ^a   Ionkin, Nikolai I ^a   Morozova, Valentina A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Finite Difference scheme; Heat Conduction equation; Necessary and sufficient stability conditions; Nonlocal boundary conditions

Indexed keywords

EID: 0141573217     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2001-0004     Document Type: Article

References (20)

1. N. V. Ardelyan and A. V. Gulin, Justification of the stability of difference scheme for the acoustic's equations, Preprint No. 96. Keldysh Inst. Appl. Math. Acad. Sci. USSR, Moscow, 1978, in Russian.
2. E. G. D'yakonov, On stability of difference schemes for some nonstationary problems, in: Topics in Numerical Analysis (J. J. H. Miller, ed.), vol. II, Academic Press, London, 1973, pp. 63-87.
3. A. V. Gulin, On stability with respect to initial data of nonselfadjoint difference schemes, Soviet. Math. Docl., 20 (1979), No. 1, pp. 96-99.
4. A. V. Gulin, Theorems on stability of nonselfadjoint difference schemes, Mat. USSR Sbornik, 110 (152) (1979), No. 2, pp. 297-303, (in Russian).
5. A. V. Gulin and A. A. Martynov, On stability conditions for a family of nonselfadjoint difference schemes, Mat. USSR Sbornik, 45 (1983), No. 4, pp. 431-437.
6. A. V. Gulin and A. A. Samarskiľ, On the stability of difference schemes with nonselfadjoint operators, Soviet. Math. Docl., 13 (1972), No. 5, pp. 1392-1395.
7. A. V. Gulin and A. A. Samarskiľ, On some results and problems of the stability theory of difference schemes, Mat. USSR Sbornik, 28 (1976), No. 3, pp. 263-290.
8. N. I. Ionkin, A problem for the heatconeluction equation with nonclassical (nonlocal) boundary condition, Preprint No. 14, Budapest, Numerikus Modzerek, 1979, in Russian.
9. P. D. Lax and R. D. Richtmyer, Survey of the stability of linear finite difference equations, Commun. Pure Appl. Math., 9 (1956), No. 2, pp. 267-293.
10. V. L. Makarov, Difference schemes for the parabolic quasilinear equations with nonlocal boundary conditions from the class of generalised solutions, in: Numerical Methods and Their Applieatiens' 84, Sophia, 1985, pp. 82-90.
11. V. S. Ryaben'kii and A. F. Filippov, Stability of Difference Equations, Band 3 of Mathematik fur Natur und Technik, VEB Deutcher Verlag, Berlin, 1960.
12. A. A. Samarskiľ, Classes of stable schemes, USSR Comput. Math. and Math. Phys., 7 (1967), No. 5, pp. 171-223.
13. A. A. Samarskiľ, Regularization of difference schemes, USSR Comput. Math. and Math. Phys., 7 (1967), No. 1, pp. 79-120.
14. A. A. Samarskiľ, Necessary and sufficient conditions for stability of two-layer difference schemes, Soviet. Math. Docl., 9 (1968), No. 4, pp. 946-950.
15. A. A. Samarskiľ, Theorie der Differenzenverfahren, Acad. Verl. Geest and Portig K. G., Leipzig, 1984.
16. A. A. Samarskiľ, Theory of difference schemes, 3rd edn., Nauka, Moscow, 1989 (in Russian).
17. A. A. Samarskiľ and A. V. Gulin, Stability of difference schemes, Nauka, Moscow, 1973, in Russian.
18. A. A. Samarskiľ, P. N. Vabishchevich, and A. V. Gulin, Stability of operator-difference schemes, Differents. Uravn., 35 (1999), No. 2, pp. 152-187, in Russian.
19. M. P. Sapagovas and R. U. Chegis, On certain boundary problems with nonlocal condition, Differents. Uravn., 23 (1987), No. 7, pp. 1268-1274, in Russian.
20. V. Thomee, Stability theory for partial difference operators, SIAM Review, 11 (1969), No. 2, pp. 152-195.