| Title:
|
$A$-stable methods of high order for Volterra integral equations (English) |
| Author:
|
Malina, Ľubor |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
20 |
| Issue:
|
5 |
| Year:
|
1975 |
| Pages:
|
336-344 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Method for numerical solution of Volterra integral equations, based on the O.I.M. methods, is suggested. It is known that the class of O.I.M. methods includes $A$-stable methods of arbitrary high order of asymptotic accuracy. In part 5, it is proved that these methods generate methods for numerical solution of Volterra equations which are also $A$-stable and of an arbitrarily high order. There is one advantage of the methods. Namely, they need no matrix inversion in the course of their numerical realization. (English) |
| Keyword:
|
$A$-stable methods |
| MSC:
|
45D05 |
| MSC:
|
45L05 |
| MSC:
|
65R05 |
| MSC:
|
65R20 |
| idZBL:
|
Zbl 0336.45016 |
| idMR:
|
MR0386320 |
| DOI:
|
10.21136/AM.1975.103599 |
| . |
| Date available:
|
2008-05-20T18:01:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103599 |
| . |
| Reference:
|
[1] Práger M., Taufer J., Vitásek E.: Overimplicit multistep methods.Aplikace matematiky 18 (1973), 399-421. MR 0366041 |
| Reference:
|
[2] de Hoog F., Weiss R.: High order methods for Volterra integral equations of the first kind.SIAM J. Numer. Anal. 10 (1973), 647-664. Zbl 0261.65086, MR 0373354, 10.1137/0710057 |
| Reference:
|
[3] de Hoog F., Weiss R.: On the solution of Volterra integral equation of the first kind.Num. Math. 21 (1973) 22-32. MR 0371114, 10.1007/BF01436183 |
| Reference:
|
[4] Noble B.: Instability when solving Volterra integral equation of the first kind by multistep methods.in Conference on the numerical solution of differential equations, Lecture notes in Mathematics 109, 23-39. MR 0273859 |
| Reference:
|
[5] Brunner H., Lambert J. D.: Stability of numerical methods for Volterra integro-differential equations.Computing 12 (1974), 75-89. Zbl 0282.65088, MR 0418490, 10.1007/BF02239501 |
| . |
