| Title:
|
Overimplicit multistep methods (English) |
| Author:
|
Práger, Milan |
| Author:
|
Taufer, Jiří |
| Author:
|
Vitásek, Emil |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
18 |
| Issue:
|
6 |
| Year:
|
1973 |
| Pages:
|
399-421 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper is concerned with the numerical solution of ordinary differential equations by a new class of methods called overimplicit multistep methods. The effort is devoted to the study of the convergence and $A$-stability of the introduced methods. $A$-stable formulae of arbitrarily high orders are shown to exist in this new class. This implies the efficiency of using these methods for stiff problems. () |
| MSC:
|
65J99 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0298.65052 |
| idMR:
|
MR0366041 |
| DOI:
|
10.21136/AM.1973.103497 |
| . |
| Date available:
|
2008-05-20T17:57:25Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103497 |
| . |
| Reference:
|
[1] I. Babuška M. Práger, E. Vitásek: Numerical processes in differential equations.Interscience publishers, London, New York, Sydney (1966). MR 0223101 |
| Reference:
|
[2] G. Birkhoff, R. S. Varga: Discretization errors for well-set Cauchy problems I.J. Math, and Phys. 44 (1965), 1-23. Zbl 0134.13406, MR 0179952, 10.1002/sapm19654411 |
| Reference:
|
[3] G. Dahlquist: A special stability problem for linear multistep methods.BIT 3 (1963), 27-43. Zbl 0123.11703, MR 0170477, 10.1007/BF01963532 |
| Reference:
|
[4] F. R. Gantmacher (Ф. Р. Гантмахер): Теория матриц.Наука, Москва (1966). Zbl 0136.00410 |
| Reference:
|
[5] P. Henrici: Discrete variable methods in ordinary differential equations.J. Wiley & Sons, Inc., New York, London (1962). Zbl 0112.34901, MR 0135729 |
| Reference:
|
[6] J. Taufer (И. Тауфер): Об одном обобщенном многошаговом методе, сб. Применение функциональных методов к краевым задачам математической физики.Новосибирск (1972). Zbl 0262.65050 |
| Reference:
|
[7] R. S. Varga: Matrix iterative analysis.Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1962). MR 0158502 |
| Reference:
|
[8] E. Vitásek (E. Витасек): Строго неявные методы для решения дифференциальных уравнений.сб. Применение функциональных методов к краевым задачам математической физики, Новосибирск (1972). |
| . |
