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Volumn 22, Issue 9, 1998, Pages 657-670

Modified Runge-Kutta Verner methods for the numerical solution of initial and boundary-value problems with engineering applications

Author keywords

Engineering applications; Phase lag; Runge Kutta methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; INITIAL VALUE PROBLEMS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0032155187     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(98)10068-9     Document Type: Article
Times cited : (10)

References (36)
  • 1
    • 0016440637 scopus 로고
    • Numerical solution of some ordinary differential equations occuring in plate deflection theory
    • Usmani R.A., Marsden M.J. Numerical solution of some ordinary differential equations occuring in plate deflection theory. J. Engrg. Math. 9:1975;1-10.
    • (1975) J. Engrg. Math. , vol.9 , pp. 1-10
    • Usmani, R.A.1    Marsden, M.J.2
  • 2
    • 0039647243 scopus 로고
    • 6) finite difference analogue for the soluitioon of some differential equations occuring in plate deflection theory
    • 6) finite difference analogue for the soluitioon of some differential equations occuring in plate deflection theory J. Inst. Maths Applics. 20:1977;331-333.
    • (1977) J. Inst. Maths Applics , vol.20 , pp. 331-333
    • Usmani, R.A.1
  • 3
    • 0039055027 scopus 로고
    • Discrete variable methods for a boundary value problem with engineering applications
    • Usmani R.A. Discrete variable methods for a boundary value problem with engineering applications. Math. Comput. 32:1978;1087-1096.
    • (1978) Math. Comput. , vol.32 , pp. 1087-1096
    • Usmani, R.A.1
  • 4
    • 0019184525 scopus 로고
    • Smooth spline solutions for boundary value problems in plate deflection theory
    • Usmani R.A., Warsi S.A. Smooth spline solutions for boundary value problems in plate deflection theory. Comput. Maths. Appl. 6:1980;205-211.
    • (1980) Comput. Maths. Appl. , vol.6 , pp. 205-211
    • Usmani, R.A.1    Warsi, S.A.2
  • 5
    • 0039647245 scopus 로고
    • Smooth spline approximations for a boundary value problem with engineering applications
    • Usmani R.A. Smooth spline approximations for a boundary value problem with engineering applications. J. Comput. Appl. Math. 6:1980;93-98.
    • (1980) J. Comput. Appl. Math. , vol.6 , pp. 93-98
    • Usmani, R.A.1
  • 7
    • 84966246792 scopus 로고
    • Five-diagonal sixth order methods for two-point boundary value problems involving fourth order differential equations
    • Katti C.P. Five-diagonal sixth order methods for two-point boundary value problems involving fourth order differential equations. Math. Comput. 35:1980;1117-1119.
    • (1980) Math. Comput. , vol.35 , pp. 1117-1119
    • Katti, C.P.1
  • 8
    • 0039647244 scopus 로고
    • Numerical solution of fourth-order ordinary differential equations
    • Jain M.K., Iyengar S.R., Saldanha I.S.V. Numerical solution of fourth-order ordinary differential equations. J. Engrg. Math. 11:1977;373-380.
    • (1977) J. Engrg. Math. , vol.11 , pp. 373-380
    • Jain, M.K.1    Iyengar, S.R.2    Saldanha, I.S.V.3
  • 9
    • 0018320891 scopus 로고
    • Finite difference methods for two-point boundary value problems involving high order differential equations
    • M Chawla M., Katti C.P. Finite difference methods for two-point boundary value problems involving high order differential equations. BIT. 19:1979;27-33.
    • (1979) BIT , vol.19 , pp. 27-33
    • M. Chawla, M.1    Katti, C.P.2
  • 10
    • 0019010803 scopus 로고
    • A one-step method for direct integration of structural dynamics equations
    • Brusa L., Nigro L. A one-step method for direct integration of structural dynamics equations. Internat. J. Numer. Methods Engrg. 15:1980;685-699.
    • (1980) Internat. J. Numer. Methods Engrg. , vol.15 , pp. 685-699
    • Brusa, L.1    Nigro, L.2
  • 11
    • 0021578695 scopus 로고
    • A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
    • Chawla M.M., Rao P.S. A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. J. Comput. Appl. Math. 11:1984;277-281.
    • (1984) J. Comput. Appl. Math. , vol.11 , pp. 277-281
    • Chawla, M.M.1    Rao, P.S.2
  • 12
    • 0022752603 scopus 로고
    • A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems II, Explicit method
    • Chawla M.M., Rao P.S. A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems II, Explicit method. J. Comput. Appl. Math. 15:1986;329-337.
    • (1986) J. Comput. Appl. Math. , vol.15 , pp. 329-337
    • Chawla, M.M.1    Rao, P.S.2
  • 15
    • 0001330331 scopus 로고
    • ″=f(x,y) via rational approximation for the cosine
    • ″=f(x,y) via rational approximation for the cosine IMA J. Numer. Anal. 9:1989;145-165.
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 145-165
    • Coleman, J.P.1
  • 17
    • 0009963675 scopus 로고
    • Predictor-corrector methods for periodic second-order initial value problems
    • van der Houwen P.J., Sommeijer B.P. Predictor-corrector methods for periodic second-order initial value problems. IMA J. Numer. Anal. 7:1987;407-422.
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 407-422
    • Van Der Houwen, P.J.1    Sommeijer, B.P.2
  • 18
    • 0023366337 scopus 로고
    • Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions
    • van der Houwen P.J., Sommeijer B.P. Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions. SIAM J. Numer. Anal. 24:1987;595-617.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 595-617
    • Van Der Houwen, P.J.1    Sommeijer, B.P.2
  • 19
    • 0000688555 scopus 로고
    • Diagonally implicit Runge-Kutta-Nystrom methods for oscillatory problems
    • van der Houwen P.J., Sommeijer B.P. Diagonally implicit Runge-Kutta-Nystrom methods for oscillatory problems. SIAM J. Numer. Anal. 26:1989;414-429.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 414-429
    • Van Der Houwen, P.J.1    Sommeijer, B.P.2
  • 22
    • 0000926830 scopus 로고
    • A four-step phase fitted method for the numerical integration of second order initial-value problems
    • Raptis A.D., Simos T.E. A four-step phase fitted method for the numerical integration of second order initial-value problems. BIT. 31:1990;89-121.
    • (1990) BIT , vol.31 , pp. 89-121
    • Raptis, A.D.1    Simos, T.E.2
  • 23
    • 38249009386 scopus 로고
    • A low order embedded Runge-Kutta method for periodic initial-value problems
    • Sideridis A.B., Simos T.E. A low order embedded Runge-Kutta method for periodic initial-value problems. J. Comput. Appl. Math. 44:1992;235-244.
    • (1992) J. Comput. Appl. Math. , vol.44 , pp. 235-244
    • Sideridis, A.B.1    Simos, T.E.2
  • 24
    • 0025596658 scopus 로고
    • Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
    • Simos T.E., Raptis A.D. Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation. Computing. 45:1990;175-181.
    • (1990) Computing , vol.45 , pp. 175-181
    • Simos, T.E.1    Raptis, A.D.2
  • 25
    • 30244538518 scopus 로고
    • A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial- value problems
    • Simos T.E. A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial- value problems. Internat. J. Comput. Math. 39:1991;135-140.
    • (1991) Internat. J. Comput. Math. , vol.39 , pp. 135-140
    • Simos, T.E.1
  • 26
    • 0021316047 scopus 로고
    • Phase properties of high order, almost P-stable formulae
    • Thomas R.M. Phase properties of high order, almost P-stable formulae. BIT. 24:1984;225-238.
    • (1984) BIT , vol.24 , pp. 225-238
    • Thomas, R.M.1
  • 27
    • 0002659592 scopus 로고
    • Runge-Kutta interpolants with minimal phase-lag
    • T.E. Simos, Runge-Kutta interpolants with minimal phase-lag, Comput. Math. Appl. 26 (1993) 43-49.
    • (1993) Comput. Math. Appl. , vol.26 , pp. 43-49
    • Simos, T.E.1
  • 28
    • 0026142627 scopus 로고
    • Some Runge-Kutta formula pairs
    • Verner J.H. Some Runge-Kutta formula pairs. SIAM J. Numer. Anal. 28:1991;496-511.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 496-511
    • Verner, J.H.1
  • 29
    • 0026736962 scopus 로고
    • Integration of Tresca and Mohr-Coulomb constitutive relations in plane strain elastoplasticity
    • Sloan S.W., Booker J.R. Integration of Tresca and Mohr-Coulomb constitutive relations in plane strain elastoplasticity. Intern. J. Numer. Meth. Engrg. 33:1992;163-196.
    • (1992) Intern. J. Numer. Meth. Engrg. , vol.33 , pp. 163-196
    • Sloan, S.W.1    Booker, J.R.2
  • 30
    • 34250486951 scopus 로고
    • Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
    • Fehlberg E. Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme. Computing. 6:1970;61-71.
    • (1970) Computing , vol.6 , pp. 61-71
    • Fehlberg, E.1
  • 32
    • 0000286593 scopus 로고
    • Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations
    • Enlgand R. Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations. Comput. J. 12:1969;166-170.
    • (1969) Comput. J. , vol.12 , pp. 166-170
    • Enlgand, R.1
  • 34
    • 0000468784 scopus 로고
    • Explicit Runge-Kutta methods with estimates of the local truncation error
    • Verner J.H. Explicit Runge-Kutta methods with estimates of the local truncation error. SIAM J. Numer. Anal. 15:1978;772-790.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 772-790
    • Verner, J.H.1
  • 35
    • 0022734765 scopus 로고
    • A reconsideration of some embedded Runge-Kutta formulae
    • Dormand J.R., Prince P.J. A reconsideration of some embedded Runge-Kutta formulae. J. Comput. Appl. Math. 15:1986;203-211.
    • (1986) J. Comput. Appl. Math. , vol.15 , pp. 203-211
    • Dormand, J.R.1    Prince, P.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.