Runge-Kutta Methods for Differential Equations with Variable Time of Impulses

被引：4

作者：

Din, Q. ^{[1
]}

Donchev, T. ^{[2
]}

Nosheen, A. ^{[3
]}

Rafaqat, M. ^{[4
]}

机构：

[1] Univ Poonch Rawalakot, Dept Math, Ravalakol, Pakistan

[2] Alexandru Ioan Cuza Univ, Dept Math, Iasi 700506, Romania

[3] Univ Sargodha, Dept Math, Sargodha, Pakistan

[4] ASSMS, Lahore, Pakistan

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2015年 / 36卷 / 06期

关键词：

34A37; 65L06; Switching surfaces; Runge-Kutta methods; Impulsive differential equations; APPROXIMATION;

D O I：

10.1080/01630563.2015.1031380

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, Runge-Kutta methods of order p are used to approximate the solutions of differential equations with variable times of impulses. It is proved that these methods have order of approximation O(h ( p )) w.r.t. the defined measure of distance. Illustrative examples with different strategies to find the events are provided.

引用

页码：777 / 791

页数：15

共 50 条

[41] Explicit A-stable rational Runge-Kutta methods for parabolic differential equations
Nakashima, M
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON PARALLEL AND DISTRIBUTED PROCESSING TECHNIQUES AND APPLICATIONS, VOLS I-V, 2000, : 2847 - 2853
[42] Preservation of quadratic invariants ofstochastic differential equations via Runge-Kutta methods
Hong, Jialin
Xu, Dongsheng
Wang, Peng
APPLIED NUMERICAL MATHEMATICS, 2015, 87 : 38 - 52
[43] Predictor-corrector methods of Runge-Kutta type for stochastic differential equations
Burrage, K
Tian, TH
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (04) : 1516 - 1537
[44] Two-stage stochastic Runge-Kutta methods for stochastic differential equations
Tian, TH
Burrage, K
BIT, 2002, 42 (03): : 625 - 643
[45] D-convergence of Runge-Kutta methods for stiff delay differential equations
Huang, CM
Fu, HY
Li, SF
Chen, GN
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2001, 19 (03) : 259 - 268
[46] Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
Wang, Qiubao
Li, Dongsong
Liu, M. Z.
CHAOS SOLITONS & FRACTALS, 2009, 42 (05) : 3087 - 3099
[47] Two-Stage Stochastic Runge-Kutta Methods for Stochastic Differential Equations
T. H. Tian
K. Burrage
BIT Numerical Mathematics, 2002, 42 : 625 - 643
[48] New stability results for Runge-Kutta methods adapted to delay differential equations
Van den Heuvel, G
APPLIED NUMERICAL MATHEMATICS, 2000, 34 (2-3) : 293 - 308
[49] HIGH ORDER CONTRACTIVE RUNGE-KUTTA METHODS FOR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS
Li, Shoufu
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) : 4290 - 4325
[50] Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations
甘四清
郑纬民
Tsinghua Science and Technology, 2004, (02) : 185 - 188

← 1 2 3 4 5 →