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

[41] A NOTE ON CONTINUOUS DEPENDENCE OF SOLUTIONS OF VOLTERRA INTEGRAL-EQUATIONS
GYLLENBERG, M
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 81 (04) : 546 - 548
[42] Dissipativity of Runge-Kutta methods for Volterra functional differential equations
Wen, Liping
Yu, Yuexin
Li, Shoufu
APPLIED NUMERICAL MATHEMATICS, 2011, 61 (03) : 368 - 381
[43] Runge-Kutta methods for monotone differential and delay equations
Kloeden, PE
Schropp, J
BIT, 2003, 43 (03): : 571 - 586
[44] Convergence of Runge-Kutta methods for delay differential equations
'T Hout, KJI
BIT NUMERICAL MATHEMATICS, 2001, 41 (02) : 322 - 344
[45] Convergence of Runge-Kutta Methods for Delay Differential Equations
K. J. In 't Hout
BIT Numerical Mathematics, 2001, 41 : 322 - 344
[46] Exponential Runge-Kutta methods for delay differential equations
Xu, Y.
Zhao, J. J.
Sui, Z. N.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2010, 80 (12) : 2350 - 2361
[47] ITERATED COLLOCATION METHODS AND THEIR DISCRETIZATIONS FOR VOLTERRA INTEGRAL-EQUATIONS
BRUNNER, H
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1984, 21 (06) : 1132 - 1145
[48] NUMERICAL-SOLUTION OF VOLTERRA INTEGRAL-EQUATIONS WITH DELAY ARGUMENTS
CAHLON, B
NACHMAN, LJ
SCHMIDT, D
JOURNAL OF INTEGRAL EQUATIONS, 1984, 7 (03): : 191 - 208
[49] Stability Analysis of Runge-Kutta Methods for Nonlinear Neutral Volterra Delay-Integro-Differential Equations
Wang, Wansheng
Li, Dongfang
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2011, 4 (04) : 537 - 561
[50] EXTENSIONS OF VOLTERRA INTEGRAL-EQUATIONS AND VOLTERRA INTEGRODIFFERENTIAL EQUATIONS
KRIVOSHEIN, LE
MANGERON, D
OGUZTORELI, MN
ROSSI, FS
ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1973, 54 (06): : 860 - 864

← 1 2 3 4 5 →