# $A$-stable methods of high order for Volterra integral equations

Aplikace matematiky (1975)

- Volume: 20, Issue: 5, page 336-344
- ISSN: 0862-7940

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topMalina, Ľubor. "$A$-stable methods of high order for Volterra integral equations." Aplikace matematiky 20.5 (1975): 336-344. <http://eudml.org/doc/14923>.

@article{Malina1975,

abstract = {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.},

author = {Malina, Ľubor},

journal = {Aplikace matematiky},

keywords = {$A$-stable methods; -Stable methods},

language = {eng},

number = {5},

pages = {336-344},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {$A$-stable methods of high order for Volterra integral equations},

url = {http://eudml.org/doc/14923},

volume = {20},

year = {1975},

}

TY - JOUR

AU - Malina, Ľubor

TI - $A$-stable methods of high order for Volterra integral equations

JO - Aplikace matematiky

PY - 1975

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 20

IS - 5

SP - 336

EP - 344

AB - 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.

LA - eng

KW - $A$-stable methods; -Stable methods

UR - http://eudml.org/doc/14923

ER -

## References

top- Práger M., Taufer J., Vitásek E., Overimplicit multistep methods, Aplikace matematiky 18 (1973), 399-421. (1973) Zbl0298.65052MR0366041
- de Hoog F., Weiss R., 10.1137/0710057, SIAM J. Numer. Anal. 10 (1973), 647-664. (1973) Zbl0261.65086MR0373354DOI10.1137/0710057
- de Hoog F., Weiss R., 10.1007/BF01436183, Num. Math. 21 (1973) 22-32. (1973) Zbl0262.65078MR0371114DOI10.1007/BF01436183
- 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. Zbl0207.17005MR0273859
- Brunner H., Lambert J. D., 10.1007/BF02239501, Computing 12 (1974), 75-89. (1974) Zbl0282.65088MR0418490DOI10.1007/BF02239501

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