A -stable methods of high order for Volterra integral equations

Ľubor Malina

Aplikace matematiky (1975)

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

Abstract

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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.

How to cite

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Malina, 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

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

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