지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 665 - 684 (20page)
이용수
초록· 키워드
오류제보하기
Runge-Kutta-NystrÄom (RKN) methods provide a popular way to solve the
initial value problem (IVP) for a system of ordinary differential equations (ODEs). Users of software are typically asked to specify a tolerance delta, that indicates in somewhat vague sense, the level of accuracy required. It is clearly important to understand the precise effect of changing delta, and to derive the strongest possible results about the behaviour of the global error that will not have regular behaviour unless an appropriate stepsize selection
formula and standard error control policy are used. Faced with this situation sufficient conditions on an algorithm that guarantee such behaviour for the global error to be asympotatically linear in delta as δ → 0 , that were first derived by Stetter. Here we extend the analysis to cover a certain class of ODEs with low-order derivative discontinuities, and the class of ODEs with constant delays. We show that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficient accurate interpolants. It is perhaps surprising that several delay ODE algorithms that have been proposed do not use sufficiently accurate interpolants to guarantee asymptotic proportionality. Our theoretical results are illustrated numerically.
목차
등록된 정보가 없습니다.
참고문헌 (26)
참고문헌 신청
A. Bellen / 1984 / One step collocation for delay di®erential equations / J. Comp. Appl. Math 10 : 275 ~ 283
A. Bellen / 1985 / A Runge-Kutta-NystrAom method for Delay Di®erential Equations, Progress in Scienti?c Computing / Numerical Boundary Value ODEs 5 : 271 ~ 283
A. Bellen / 1985 / Numerical solution of delay di®erential equations by uni-form corrections to an implicit Runge-Kutta method / Numer. Math 47 : 301 ~ 316
A. Marthinsen / 1994 / Continuous Extensions to NystrAom methods for the explicit solu-tion of second order initial value problems
A. V. Kim / 1997 / Numerical methods for time-delay systems on the basis of i-smooth analysis, Proceedings of the 15th World Congress on Scienti?c Computa-tion, Modelling an
A. Bellen / 1985 / A Runge-Kutta-NystrAom method for Delay Di®erential Equations, Progress in Scienti?c Computing / Numerical Boundary Value ODEs 5 : 271 ~ 283
A. Bellen / 1985 / Numerical solution of delay di®erential equations by uni-form corrections to an implicit Runge-Kutta method / Numer. Math 47 : 301 ~ 316
A. Marthinsen / 1994 / Continuous Extensions to NystrAom methods for the explicit solu-tion of second order initial value problems
A. V. Kim / 1997 / Numerical methods for time-delay systems on the basis of i-smooth analysis, Proceedings of the 15th World Congress on Scienti?c Computa-tion, Modelling an
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
A LOCAL-GLOBAL VERSION OF A STEPSIZE CONTROL FOR RUNGE-KUTTA METHODS
The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A
2000 .01
-
A NEW METHOD FOR SOLVING THE NONLINEAR SECOND-ORDER BOUNDARY VALUE DIFFERENTIAL EQUATIONS
The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A
2000 .01
-
An error embedded Runge-Kutta method for initial value problems
Kyungpook Mathematical Journal
2016 .01
-
A NEW FIFTH-ORDER WEIGHTED RUNGE-KUTTA ALGORITHM BASED ON HERONIAN MEAN FOR INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS
Journal of applied mathematics & informatics
2017 .01
-
Error Control Strategy in Error Correction Methods
Kyungpook Mathematical Journal
2015 .01
-
A NEW APPROACH FOR ASYMPTOTIC STABILITY A SYSTEM OF THE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
Journal of applied mathematics & computing
2007 .01
-
Global Existence of Strong Solution for Some Controlled Ode-Pde Systems
East Asian Mathematical Journal
2019 .01
-
A LOCAL-GLOBAL STEPSIZE CONTROL FOR MULTISTEP METHODS APPLIED TO SEMI-EXPLICIT INDEX 1 DIFFERENTIAL-ALGEBRAIC EUATIONS
The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A
1999 .01
-
VALUE FUNCTIONS AND ERROR BOUNDS OF TRUST REGION METHODS
Journal of applied mathematics & computing
2007 .01
-
부유분진측정기(PM10) 관측 자료 실시간 품질관리 알고리즘 개발 및 평가
대기
2016 .12
-
HOPF BIFURCATION IN NUMERICAL APPROXIMATION FOR DELAY DIFFERENTIAL EQUATIONS
Journal of applied mathematics & computing
2004 .01
-
NECESSARY CONDITIONS FOR OPTIMAL CONTROL GOVERNED BY SOME ODE-PDE SYSTEMS
East Asian Mathematical Journal
2019 .01
-
A DELAY-DEPENDENT STABILITY CRITERION IN TIME-DELAY SYSTEM
JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
2005 .12
-
ON DELTA ALPHA DERIVATIVE ON TIME SCALES
충청수학회지
2016 .01
-
A NON-ASYMPTOTIC METHOD FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS
Journal of applied mathematics & informatics
2014 .01
-
A SCHWARZ METHOD FOR FOURTH-ORDER SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEM WITH DISCONTINUOUS SOURCE TERM
Journal of applied mathematics & informatics
2016 .01
-
OSCILLATION AND ASYMPTOTIC BEHAVIOR FOR DELAY DIFFERENTIAL EQUATIONS
The Korean journal of computational & applied mathematics, 한국전산응용수학술지 Series A
2000 .01
-
DELAY-DEPENDENT GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF DELAYED CELLULAR NEURAL NETWORKS
Journal of applied mathematics & informatics
2010 .01
-
ON STABILITY AND BIFURCATION OF PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS
Journal of applied mathematics & computing
2005 .01
-
Simple ECEM Algorithms Using Function Values Only
Kyungpook Mathematical Journal
2013 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0