메뉴 건너뛰기




Volumn 173, Issue 3, 2005, Pages 115-130

Stability and phase-lag analysis of explicit Runge-Kutta methods with variable coefficients for oscillatory problems

Author keywords

Exponential fitting; Numerical methods for ODEs; Phase fitting; Phase lag analysis; Runge Kutta methods; Stability analysis

Indexed keywords

ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EID: 27944439394     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2005.07.007     Document Type: Article
Times cited : (48)

References (33)
  • 1
    • 0000825514 scopus 로고
    • Runge-Kutta algorithms for oscillatory problems
    • D.G. Bettis Runge-Kutta algorithms for oscillatory problems ZAMP 30 1979 699 704
    • (1979) ZAMP , vol.30 , pp. 699-704
    • Bettis, D.G.1
  • 3
    • 0032183736 scopus 로고    scopus 로고
    • Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based in trigonometric polynomials
    • B. Paternoster Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based in trigonometric polynomials Appl. Numer. Math. 28 1998 401 412
    • (1998) Appl. Numer. Math. , vol.28 , pp. 401-412
    • Paternoster, B.1
  • 4
    • 0034512338 scopus 로고    scopus 로고
    • Mixed collocation methods for y″ = f(x, y)
    • J.P. Coleman, and S.C. Duxbury Mixed collocation methods for y″ = f(x, y) J. Comput. Appl. Math. 126 2000 47 75
    • (2000) J. Comput. Appl. Math. , vol.126 , pp. 47-75
    • Coleman, J.P.1    Duxbury, S.C.2
  • 7
    • 0037114704 scopus 로고    scopus 로고
    • An embedded pair of exponentially fitted explicit Runge-Kutta methods
    • J.M. Franco An embedded pair of exponentially fitted explicit Runge-Kutta methods J. Comput. Appl. Math. 149 2002 407 414
    • (2002) J. Comput. Appl. Math. , vol.149 , pp. 407-414
    • Franco, J.M.1
  • 8
    • 14044278670 scopus 로고    scopus 로고
    • A trigonometrically fitted Runge-Kutta method for the numerical solution of orbital problems
    • Z.A. Anastassi, and T.E. Simos A trigonometrically fitted Runge-Kutta method for the numerical solution of orbital problems New Astronomy 10 2005 301 309
    • (2005) New Astronomy , vol.10 , pp. 301-309
    • Anastassi, Z.A.1    Simos, T.E.2
  • 9
    • 0000926830 scopus 로고
    • A four-step phase-fitted method for the numerical integration of the Schrödinger equation
    • A.D. Raptis, and T.E. Simos A four-step phase-fitted method for the numerical integration of the Schrödinger equation BIT 31 1991 160 168
    • (1991) BIT , vol.31 , pp. 160-168
    • Raptis, A.D.1    Simos, T.E.2
  • 10
    • 27944475127 scopus 로고
    • A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution
    • T.E. Simos A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution Comput. Math. Appl. 25 1993 95 101
    • (1993) Comput. Math. Appl. , vol.25 , pp. 95-101
    • Simos, T.E.1
  • 11
    • 0032300656 scopus 로고    scopus 로고
    • An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
    • T.E. Simos An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions Comput. Phys. Comm. 115 1998 1 8
    • (1998) Comput. Phys. Comm. , vol.115 , pp. 1-8
    • Simos, T.E.1
  • 12
    • 0034555538 scopus 로고    scopus 로고
    • An embedded Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation
    • T.E. Simos An embedded Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation Internat. J. Modern Phys. C 11 2000 1115 1133
    • (2000) Internat. J. Modern Phys. C , vol.11 , pp. 1115-1133
    • Simos, T.E.1
  • 13
    • 0034744534 scopus 로고    scopus 로고
    • A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems
    • T.E. Simos, and Jesús Vigo Aguiar A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems Comput. Chem. 25 2001 275 281
    • (2001) Comput. Chem. , vol.25 , pp. 275-281
    • Simos, T.E.1    Aguiar, J.V.2
  • 14
    • 0035384934 scopus 로고    scopus 로고
    • A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
    • T.E. Simos, and Jesús Vigo Aguiar A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation J. Math. Chem. 30 2001 121 131
    • (2001) J. Math. Chem. , vol.30 , pp. 121-131
    • Simos, T.E.1    Aguiar, J.V.2
  • 15
    • 0037109217 scopus 로고    scopus 로고
    • Optimized Runge-Kutta pairs for problems with oscillating solutions
    • Ch. Tsitouras, and T.E. Simos Optimized Runge-Kutta pairs for problems with oscillating solutions J. Comput. Appl. Math. 147 2002 397 409
    • (2002) J. Comput. Appl. Math. , vol.147 , pp. 397-409
    • Tsitouras, Ch.1    Simos, T.E.2
  • 16
    • 7444231046 scopus 로고    scopus 로고
    • A dispersive-fitted and dissipative-fitted explicit Runge-Kutta method for the numerical solution of orbital problems
    • Z.A. Anastassi, and T.E. Simos A dispersive-fitted and dissipative-fitted explicit Runge-Kutta method for the numerical solution of orbital problems New Astronomy 10 2004 31 37
    • (2004) New Astronomy , vol.10 , pp. 31-37
    • Anastassi, Z.A.1    Simos, T.E.2
  • 17
    • 11044230429 scopus 로고    scopus 로고
    • An optimized Runge-Kutta method for the solution of orbital problems
    • Z.A. Anastassi, and T.E. Simos An optimized Runge-Kutta method for the solution of orbital problems J. Comput. Appl. Math. 175 2005 1 9
    • (2005) J. Comput. Appl. Math. , vol.175 , pp. 1-9
    • Anastassi, Z.A.1    Simos, T.E.2
  • 18
    • 17744361851 scopus 로고    scopus 로고
    • A trigonometrically fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
    • Z.A. Anastassi, and T.E. Simos A trigonometrically fitted Runge-Kutta method for the numerical solution of the Schrödinger equation J. Math. Chem. 37 2005 281 293
    • (2005) J. Math. Chem. , vol.37 , pp. 281-293
    • Anastassi, Z.A.1    Simos, T.E.2
  • 19
    • 13844284351 scopus 로고    scopus 로고
    • Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
    • H. Van de Vyver Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation Comput. Phys. Comm. 166 2005 109 122
    • (2005) Comput. Phys. Comm. , vol.166 , pp. 109-122
    • Van De Vyver, H.1
  • 20
    • 22944432161 scopus 로고    scopus 로고
    • An embedded 5(4) pair of modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
    • H. Van de Vyver An embedded 5(4) pair of modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation Internat. J. Modern Phys. C 16 2005 879 894
    • (2005) Internat. J. Modern Phys. C , vol.16 , pp. 879-894
    • Van De Vyver, H.1
  • 21
    • 31144468206 scopus 로고    scopus 로고
    • Modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
    • in press (available via Science Direct)
    • H. Van de Vyver, Modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation, Appl. Math. Comput., in press (available via Science Direct)
    • Appl. Math. Comput.
    • Van De Vyver, H.1
  • 23
    • 0034509539 scopus 로고    scopus 로고
    • A phase-fitted collocation-based Runge-Kutta-Nyström method
    • B. Paternoster A phase-fitted collocation-based Runge-Kutta-Nyström method Appl. Numer. Math. 35 2000 339 355
    • (2000) Appl. Numer. Math. , vol.35 , pp. 339-355
    • Paternoster, B.1
  • 24
    • 0000554052 scopus 로고
    • On the numerical integration of perturbed oscillators
    • G. Scheifele On the numerical integration of perturbed oscillators ZAMP 22 1971 186 210
    • (1971) ZAMP , vol.22 , pp. 186-210
    • Scheifele, G.1
  • 25
    • 0040531663 scopus 로고    scopus 로고
    • A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators
    • A.B. González, P. Martín, and J.M. Farto A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators Numer. Math. 82 1999 635 646
    • (1999) Numer. Math. , vol.82 , pp. 635-646
    • González, A.B.1    Martín, P.2    Farto, J.M.3
  • 26
    • 0036719933 scopus 로고    scopus 로고
    • Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
    • J.M. Franco Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators Comput. Phys. Comm. 147 2002 770 787
    • (2002) Comput. Phys. Comm. , vol.147 , pp. 770-787
    • Franco, J.M.1
  • 27
    • 0036679951 scopus 로고    scopus 로고
    • New methods for oscillatory problems based on classical codes
    • A. García, P. Martín, and A.B. González New methods for oscillatory problems based on classical codes Appl. Numer. Math. 42 2002 141 157
    • (2002) Appl. Numer. Math. , vol.42 , pp. 141-157
    • García, A.1    Martín, P.2    González, A.B.3
  • 28
    • 0005285043 scopus 로고    scopus 로고
    • P-stability and exponential fitting methods for y″ = f(x, y)
    • J.P. Coleman, and L.Gr. Ixaru P-stability and exponential fitting methods for y″ = f(x, y) IMA J. Numer. Anal. 16 1996 179 199
    • (1996) IMA J. Numer. Anal. , vol.16 , pp. 179-199
    • Coleman, J.P.1    Ixaru, L.Gr.2
  • 29
    • 14844290293 scopus 로고    scopus 로고
    • Stability regions of one step mixed collocation methods for y″ = f(x, y)
    • M. Carpentieri, and B. Paternoster Stability regions of one step mixed collocation methods for y″ = f(x, y) Appl. Numer. Math. 53 2005 201 212
    • (2005) Appl. Numer. Math. , vol.53 , pp. 201-212
    • Carpentieri, M.1    Paternoster, B.2
  • 30
    • 85066967669 scopus 로고    scopus 로고
    • On the generation of P-stable exponentially fitted Runge-Kutta- Nyström methods by exponentially fitted Runge-Kutta methods
    • in press (available via Science Direct)
    • H. Van de Vyver, On the generation of P-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods, J. Comput. Appl. Math., in press (available via Science Direct)
    • J. Comput. Appl. Math.
    • Van De Vyver, H.1
  • 31
    • 0019705482 scopus 로고
    • Stability of linear multistep methods on the imaginary axis
    • K. Dekker Stability of linear multistep methods on the imaginary axis BIT 21 1981 66 79
    • (1981) BIT , vol.21 , pp. 66-79
    • Dekker, K.1
  • 32
    • 8144230726 scopus 로고    scopus 로고
    • Stability of explicit ARKN methods for perturbed oscillators
    • J.M. Franco Stability of explicit ARKN methods for perturbed oscillators J. Comput. Appl. Math. 173 2005 389 396
    • (2005) J. Comput. Appl. Math. , vol.173 , pp. 389-396
    • Franco, J.M.1
  • 33
    • 0023366337 scopus 로고
    • Explicit Runge-Kutta(-Nyström) methods with reduced phase errors for computing oscillating solution
    • P.J. van der Houwen, and B.P. Sommeijer Explicit Runge-Kutta(- Nyström) methods with reduced phase errors for computing oscillating solution 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.