| Title:
|
Convergence of numerical methods for systems of neutral functional-differential-algebraic equations (English) |
| Author:
|
Jankowski, Tadeusz |
| Author:
|
Kwapisz, Marian |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
6 |
| Year:
|
1995 |
| Pages:
|
457-472 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved. (English) |
| Keyword:
|
neutral functional-differential-algebraic systems |
| Keyword:
|
consistency |
| Keyword:
|
convergence |
| MSC:
|
34K40 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0853.65077 |
| idMR:
|
MR1353973 |
| DOI:
|
10.21136/AM.1995.134307 |
| . |
| Date available:
|
2009-09-22T17:49:39Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134307 |
| . |
| Reference:
|
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| Reference:
|
[2] S. L. Campbell: Singular Systems of Differential Equations.Pitman, London, 1980. Zbl 0419.34007 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[7] C. W. Gear, L. R. Petzold: ODE methods for the solution of differential/algebraic systems.SIAM J. Numer. Anal. 21 (1984), 716–728. MR 0749366, 10.1137/0721048 |
| Reference:
|
[8] E. Griepentrog, R. März: Differential-Algebraic Equations and Their Numerical Treatment.Teubner-Verlag, Leipzig, 1986. MR 0881052 |
| Reference:
|
[9] E. Hairer, Ch. Lubich, M. Roche: The numerical solution of differential-algebraic systems by Runge-Kutta methods.Lecture Notes in Mathematics Nr. 1409, Springer-Verlag, Berlin, Heidelberg, New York, 1989. MR 1027594 |
| Reference:
|
[10] Z. Jackiewicz: One-step methods of any order for neutral functional differential equations.SIAM J. Numer. Anal. 21 (1984), 486–511. Zbl 0562.65056, MR 0744170, 10.1137/0721036 |
| Reference:
|
[11] Z. Jackiewicz, M. Kwapisz: Convergence of waveform relaxation methods for differential algebraic systems.SIAM J. Numer. Anal., In press. MR 1427465 |
| Reference:
|
[12] T. Jankowski: Existence, uniqueness and approximate solutions of problems with a parameter.Zesz. Nauk. Politech. Gdańsk, Mat. 16 (1993), 3–167. Zbl 0893.34062 |
| Reference:
|
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| Reference:
|
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