Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

Z. W. Yang; M. Z. Liu; Juan J. Nieto

doi:10.1016/j.cam.2009.08.105

Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

Z. W. Yang^*
, M. Z. Liu
, Juan J. Nieto

^*Corresponding author for this work

School of Mathematics

University of Santiago de Compostela
Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In this paper we deal with the numerical solutions of Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green's function. It is shown that Runge-Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.

Original language	English
Pages (from-to)	990-1004
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	233
Issue number	4
DOIs	https://doi.org/10.1016/j.cam.2009.08.105
State	Published - 15 Dec 2009

Keywords

Comparison theorems
Differential equations with piecewise constant arguments
Green's function
Runge-Kutta methods

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10.1016/j.cam.2009.08.105

Cite this

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title = "Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments",

abstract = "In this paper we deal with the numerical solutions of Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green's function. It is shown that Runge-Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.",

keywords = "Comparison theorems, Differential equations with piecewise constant arguments, Green's function, Runge-Kutta methods",

author = "Yang, \{Z. W.\} and Liu, \{M. Z.\} and Nieto, \{Juan J.\}",

year = "2009",

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AU - Yang, Z. W.

AU - Liu, M. Z.

AU - Nieto, Juan J.

PY - 2009/12/15

Y1 - 2009/12/15

N2 - In this paper we deal with the numerical solutions of Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green's function. It is shown that Runge-Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.

AB - In this paper we deal with the numerical solutions of Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green's function. It is shown that Runge-Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.

KW - Comparison theorems

KW - Differential equations with piecewise constant arguments

KW - Green's function

KW - Runge-Kutta methods

UR - https://www.scopus.com/pages/publications/70349730230

U2 - 10.1016/j.cam.2009.08.105

DO - 10.1016/j.cam.2009.08.105

M3 - 文章

AN - SCOPUS:70349730230

SN - 0377-0427

VL - 233

SP - 990

EP - 1004

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 4

ER -

Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

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Keywords

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