CONTINUOUS VOLTERRA-RUNGE-KUTTA METHODS FOR INTEGRAL-EQUATIONS WITH PURE DELAY

被引：9

作者：

BADDOUR, N

BRUNNER, H

机构：

[1] Dept. of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, A1C 5S7, Newfoundland

来源：

COMPUTING | 1993年 / 50卷 / 03期

关键词：

VOLTERRA INTEGRAL EQUATIONS WITH DELAY; COLLOCATION; CONTINUOUS RUNGE-KUTTA METHODS; SUPERCONVERGENCE;

D O I：

10.1007/BF02243812

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In the following we give an analysis of the local superconvergence properties of piecewise polynomial collocation methods and related continuous Runge-Kutta-type methods for Volterra integral equations with constant delay. We show in particular that (in contrast to delay differential equations) collocation at the Gauss points does not lead to higher-order convergence and thus m-stage Gauss-Runge-Kutta methods for delay Volterra equations do not possess the order p = 2m.

引用

页码：213 / 227

页数：15

共 50 条

[1] COLLOCATION AND CONTINUOUS IMPLICIT RUNGE-KUTTA METHODS FOR A CLASS OF DELAY VOLTERRA INTEGRAL-EQUATIONS
BRUNNER, H
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1994, 53 (01) : 61 - 72
[2] ON THE STABILITY OF VOLTERRA-RUNGE-KUTTA METHODS
HAIRER, E
LUBICH, C
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1984, 21 (01) : 123 - 135
[3] ON THE STABILITY OF RUNGE-KUTTA METHODS FOR DELAY INTEGRAL-EQUATIONS
VERMIGLIO, R
NUMERISCHE MATHEMATIK, 1992, 61 (04) : 561 - 577
[4] IMPLICIT RUNGE-KUTTA METHODS FOR SECOND KIND VOLTERRA INTEGRAL-EQUATIONS
DE HOOG, F
WEISS, R
NUMERISCHE MATHEMATIK, 1974, 23 (03) : 199 - 213
[5] STABILITY OF PARALLEL VOLTERRA-RUNGE-KUTTA METHODS
CRISCI, MR
RUSSO, E
VANDERHOUWEN, PJ
VECCHIO, A
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1993, 45 (1-2) : 169 - 180
[6] NATURAL CONTINUOUS EXTENSIONS OF RUNGE-KUTTA METHODS FOR VOLTERRA INTEGRAL-EQUATIONS OF THE 2ND KIND AND THEIR APPLICATIONS
BELLEN, A
JACKIEWICZ, Z
VERMIGLIO, R
ZENNARO, M
MATHEMATICS OF COMPUTATION, 1989, 52 (185) : 49 - 63
[7] STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR VOLTERRA INTEGRAL-EQUATIONS OF THE 2ND KIND
BELLEN, A
JACKIEWICZ, Z
VERMIGLIO, R
ZENNARO, M
IMA JOURNAL OF NUMERICAL ANALYSIS, 1990, 10 (01) : 103 - 118
[8] Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay
Enright, WH
Hu, M
APPLIED NUMERICAL MATHEMATICS, 1997, 24 (2-3) : 175 - 190
[9] Highly stable Runge-Kutta methods for Volterra integral equations
Izzo, G.
Russo, E.
Chiapparelli, C.
APPLIED NUMERICAL MATHEMATICS, 2012, 62 (08) : 1002 - 1013
[10] IMPLICIT RUNGE KUTTA METHODS FOR SECOND KIND VOLTERRA INTEGRAL EQUATIONS
DEHOOG, F
WEISS, R
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 18 (06): : 964 - &

← 1 2 3 4 5 →