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Volumn 103, Issue 4, 2006, Pages 611-629

Nonlinear stability of general linear methods

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EID: 33744730778     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-006-0011-8     Document Type: Article
Times cited : (15)

References (20)
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    • Brune, O.1
  • 2
    • 0002351173 scopus 로고
    • Stability criteria for implicit Runge-Kutta methods
    • Burrage, K., Butcher, J.C.: Stability criteria for implicit Runge-Kutta methods. SIAM J Numer Anal, 20, 185-203, (1979)
    • (1979) SIAM J Numer Anal , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2
  • 3
    • 0001356367 scopus 로고
    • Non-linear stability of a general class of differential equation methods
    • Burrage, K., Butcher, J.C.: Non-linear stability of a general class of differential equation methods. BIT 20, 185-203, (1980)
    • (1980) BIT , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2
  • 4
    • 38249024016 scopus 로고
    • Efficiently implementable multivalue methods for solving stiff ordinary differential equations
    • Burrage, K., Chipman, F.H.: Efficiently implementable multivalue methods for solving stiff ordinary differential equations. Appl Numer Math 5, 23-40, (1989)
    • (1989) Appl Numer Math , vol.5 , pp. 23-40
    • Burrage, K.1    Chipman, F.H.2
  • 5
    • 84958480009 scopus 로고
    • On Runge-Kutta processes of high order
    • Butcher, J. C.: On Runge-Kutta processes of high order. J Austral Math Soc 3, 179-194, (1964)
    • (1964) J Austral Math Soc , vol.3 , pp. 179-194
    • Butcher, J.C.1
  • 6
    • 1542666003 scopus 로고
    • Linear and nonlinear stability for general linear methods
    • Butcher, J.C.: Linear and nonlinear stability for general linear methods. BIT 27, 182-189, (1987)
    • (1987) BIT , vol.27 , pp. 182-189
    • Butcher, J.C.1
  • 7
    • 33645019289 scopus 로고
    • The equivalence of algebraic stability and AN-stability
    • Butcher, J.C.: The equivalence of algebraic stability and AN-stability. BIT 27, 510-533, (1987)
    • (1987) BIT , vol.27 , pp. 510-533
    • Butcher, J.C.1
  • 8
    • 0000005117 scopus 로고
    • G-stability is equivalent to A-stability
    • Dahlquist, G.: G-stability is equivalent to A-stability, BIT 18, 384-401, (1978)
    • (1978) BIT , vol.18 , pp. 384-401
    • Dahlquist, G.1
  • 10
    • 0018991720 scopus 로고
    • A family of embedded Runge-Kutta formulae
    • Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. J Comp Appl Math 6, 19-26, (1980)
    • (1980) J Comp Appl Math , vol.6 , pp. 19-26
    • Dormand, J.R.1    Prince, P.J.2
  • 15
    • 0000430077 scopus 로고
    • Discrete positive-real functions and their application to system stability
    • Hitz, L., Anderson, B.D.O.: Discrete positive-real functions and their application to system stability. Proc. IEEE 116, 153-156, (1969)
    • (1969) Proc. IEEE , vol.116 , pp. 153-156
    • Hitz, L.1    Anderson, B.D.O.2
  • 16
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    • The regeneration theory
    • Nyquist, H.: The regeneration theory. Bell Syst Tech J 11, 126-147, (1932)
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  • 17
    • 0018310217 scopus 로고
    • A necessary condition for B-stability
    • Scherer, R.: A necessary condition for B-stability. BIT 19, 111-116. (1979)
    • (1979) BIT , vol.19 , pp. 111-116
    • Scherer, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.