| Title:
|
Stability of iterative schemes for nonselfadjoint equations (English) |
| Author:
|
Gupta, Murli M. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
3 |
| Year:
|
1976 |
| Pages:
|
173-184 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $A$ be a nonselfadjoint positive operator in a real Hilbert space. This paper deals with the stability of a class of iterative schemes used to solve the operator equation $Au=f$. A corresponding class of parabolic equations can also be solved by means of these iterative schemes. Several sufficient conditions of stability are obtained which are expressed in terms of known operators and can be used a priori. The results can be applied to problems with variable coefficients and initial-boundary value problems. () |
| MSC:
|
65J05 |
| MSC:
|
65M12 |
| idZBL:
|
Zbl 0343.65037 |
| idMR:
|
MR0403209 |
| DOI:
|
10.21136/AM.1976.103637 |
| . |
| Date available:
|
2008-05-20T18:04:40Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103637 |
| . |
| Reference:
|
[1] J. E. Gunn: The Solution of elliptic difference equations by semiexplicit iterative techniques.SIAM J. Numer. Anal. 2, 24-45 (1964). MR 0179962 |
| Reference:
|
[2] M. M. Gupta: Convergence and stability of finite difference schemes for some elliptic equations.Ph. D. thesis, University of Saskatchewan, Saskatoon, Canada (1971). MR 2621802 |
| Reference:
|
[3] L. V. Kantorovich G. P. Akilov: Functional analysis in normed spaces.New York: Pergamon Press 1964. MR 0213845 |
| Reference:
|
[4] H. O. Kreiss: Über die Stabilitätsdefinition für Differenzengleichungen die partieile Differentialgleichungen approximieren.Nordisk Tidskr. Informations - Behandling (BIT) 2, 153-181 (1962). MR 0165712 |
| Reference:
|
[5] P. D. Lax, and B. Wendroff: Difference schemes for hyperbolic equations with high order of accuracy.Comm. Pure Appl. Math. 17, 381-398 (1964). MR 0170484, 10.1002/cpa.3160170311 |
| Reference:
|
[6] G. G. O'Brian M. A. Hyman, and S. Kaplan: A study of the numerical solution of partial differential equations.J. Math, and Phys. 29, 223 - 251 (1951). MR 0040805 |
| Reference:
|
[7] R. D. Richtmyer, K. W. Morton: Difference methods for initialvalue problems.2nd ed., New York: Interscience 1967. |
| Reference:
|
[8] V. S. Ryabenkii, and A. F. Filippov: Über die Stabilität von Differenzengleichungen.Berlin; Deutscher Verlag der Wissenschaften 1960. MR 0123106 |
| Reference:
|
[9] A. A. Samarskii: Classes of Stable Schemes.Ž. Vyčisl. Mat. i Mat. Fiz. 7, 1096-1133 (1967). MR 0221792 |
| Reference:
|
[10] A. A. Samarskii: Necessary and Sufficient conditions for the stability of two-layer difference schemes.Soviet Math. Dokl. 9, 946-950 (1968). |
| Reference:
|
[11] A. A. Samarskii: Two layer iteration schemes for nonselfadjoint equations.Soviet Math. Dokl. 10, 554-558 (1969). |
| Reference:
|
[12] V. Thomée: Stability theory for partial difference operators.SIAM Rev. 11, 152-195 (1969). MR 0250505, 10.1137/1011033 |
| . |
