Article
Full entry |
PDF
(1.5 MB)
Feedback
PDF
(1.5 MB)
Feedback
Keywords:
$A$-stable methods
$A$-stable methods
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.
References:
[1] Práger M., Taufer J., Vitásek E.: Overimplicit multistep methods. Aplikace matematiky 18 (1973), 399-421. MR 0366041
[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. DOI 10.1137/0710057 | MR 0373354 | Zbl 0261.65086
[3] de Hoog F., Weiss R.: On the solution of Volterra integral equation of the first kind. Num. Math. 21 (1973) 22-32. DOI 10.1007/BF01436183 | MR 0371114
[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
[5] Brunner H., Lambert J. D.: Stability of numerical methods for Volterra integro-differential equations. Computing 12 (1974), 75-89. DOI 10.1007/BF02239501 | MR 0418490 | Zbl 0282.65088
Search
Partner of
