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Volumn 175, Issue 1 SPEC. ISS., 2005, Pages 137-147

A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions

Author keywords

Adams Bashforth methods; Adams Moulton methods; Initial value problems (IVPs); Multistep methods; Numerical solution; Predictor corrector (P C) methods; Trigonometric fitting

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; FUNCTION EVALUATION; NONLINEAR EQUATIONS; RUNGE KUTTA METHODS;

EID: 11044230652     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.06.014     Document Type: Article
Times cited : (163)

References (29)
  • 1
    • 0002207932 scopus 로고    scopus 로고
    • Embedded methods for the numerical solution of the Schrödinger equation
    • G. Avdelas T.E. Simos Embedded methods for the numerical solution of the Schrödinger equation Comput. Math. Appl. 31 1996 85-102
    • (1996) Comput. Math. Appl. , vol.31 , pp. 85-102
    • Avdelas, G.1    Simos, T.E.2
  • 2
    • 0030211501 scopus 로고    scopus 로고
    • A generator of high-order embedded P-stable method for the numerical solution of the Schrödinger equation
    • G. Avdelas T.E. Simos A generator of high-order embedded P-stable method for the numerical solution of the Schrödinger equation J. Comput. Appl. Math. 72 1996 345-358
    • (1996) J. Comput. Appl. Math. , vol.72 , pp. 345-358
    • Avdelas, G.1    Simos, T.E.2
  • 3
    • 0034229908 scopus 로고    scopus 로고
    • Dissipative high phase-lag order Numerov-type methods for the numerical solution of the Schrödinger equation
    • G. Avdelas T.E. Simos Dissipative high phase-lag order Numerov-type methods for the numerical solution of the Schrödinger equation Phys. Rev. E 62 2000 1375-1381
    • (2000) Phys. Rev. E , vol.62 , pp. 1375-1381
    • Avdelas, G.1    Simos, T.E.2
  • 5
    • 0242624843 scopus 로고    scopus 로고
    • A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators
    • J.M. Franco A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators J. Comput. Appl. Math. 161 2003 283-293
    • (2003) J. Comput. Appl. Math. , vol.161 , pp. 283-293
    • Franco, J.M.1
  • 6
    • 3142599427 scopus 로고    scopus 로고
    • Runge-Kutta methods adapted to the numerical integration of oscillatory problems
    • J.M. Franco, Runge-Kutta methods adapted to the numerical integration of oscillatory problems, Appl. Numer. Math. 50 (2004) 427-443.
    • (2004) Appl. Numer. Math. , vol.50 , pp. 427-443
    • Franco, J.M.1
  • 9
    • 0000913326 scopus 로고    scopus 로고
    • On the construction of exponentially-fitted methods for the numerical solution of the Schrödinger equation
    • A. Konguetsof T.E. Simos On the construction of exponentially-fitted methods for the numerical solution of the Schrödinger equation J. Comput. Methods Sci. Eng. 1 2001 143-165
    • (2001) J. Comput. Methods Sci. Eng. , vol.1 , pp. 143-165
    • Konguetsof, A.1    Simos, T.E.2
  • 12
    • 34250466523 scopus 로고
    • Chebyshevian multistep methods for ordinary differential equations
    • T. Lyche Chebyshevian multistep methods for ordinary differential equations Numer. Math. 10 1972 65-75
    • (1972) Numer. Math. , vol.10 , pp. 65-75
    • Lyche, T.1
  • 13
    • 85050061009 scopus 로고    scopus 로고
    • (Eds.) New Methods in Computational Quantum Mechanics, Wiley, New York
    • I. Prigogine, S. Rice (Eds.), Advances in Chemical Physics, Vol. 93, New Methods in Computational Quantum Mechanics, Wiley, New York, 1997
    • (1997) Advances in Chemical Physics , vol.93
    • Prigogine, I.1    Rice, S.2
  • 14
    • 0342924525 scopus 로고
    • Advanced step-point methods for the solution of initial value problems
    • Ph.D. Thesis, Imperial College, University of London
    • G. Psihoyios, Advanced step-point methods for the solution of initial value problems, Ph.D. Thesis, Imperial College, University of London, 1995.
    • (1995)
    • Psihoyios, G.1
  • 15
    • 0042228856 scopus 로고    scopus 로고
    • Exponentially and trigonometrically-fitted explicit advanced step-point (EAS) methods for IVPs with oscillating solution
    • G. Psihoyios T.E. Simos Exponentially and trigonometrically-fitted explicit advanced step-point (EAS) methods for IVPs with oscillating solution Internat. J. Modern Phys. C 14 2 2003 175-184
    • (2003) Internat. J. Modern Phys. C , vol.14 , Issue.2 , pp. 175-184
    • Psihoyios, G.1    Simos, T.E.2
  • 16
    • 0043287096 scopus 로고    scopus 로고
    • Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions
    • G. Psihoyios T.E. Simos Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions J. Comput. Appl. Math. 158 1 2003 135-144
    • (2003) J. Comput. Appl. Math. , vol.158 , Issue.1 , pp. 135-144
    • Psihoyios, G.1    Simos, T.E.2
  • 17
    • 0000613873 scopus 로고
    • Symmetric multistep methods for the numerical integration of planetary orbits
    • G.D. Quinlan S. Tremaine Symmetric multistep methods for the numerical integration of planetary orbits Astronom. J. 100 1990 1694-1700
    • (1990) Astronom. J. , vol.100 , pp. 1694-1700
    • Quinlan, G.D.1    Tremaine, S.2
  • 18
    • 0001176928 scopus 로고
    • Exponential multistep methods for ordinary differential equations
    • A.D. Raptis Exponential multistep methods for ordinary differential equations Bull. Greek Math. Soc. 25 1984 113-126
    • (1984) Bull. Greek Math. Soc. , vol.25 , pp. 113-126
    • Raptis, A.D.1
  • 19
    • 0002481902 scopus 로고
    • Exponential-fitting methods for the numerical solution of the Schrödinger equation
    • A.D. Raptis A.C. Allison Exponential-fitting methods for the numerical solution of the Schrödinger equation Comput. Phys. Comm. 14 1978 1-5
    • (1978) Comput. Phys. Comm. , vol.14 , pp. 1-5
    • Raptis, A.D.1    Allison, A.C.2
  • 21
    • 0003464948 scopus 로고
    • Numerical solution of ordinary differential equations with periodical solution
    • Doctoral Dissertation, National Technical University of Athens, Greece (in Greek)
    • T.E. Simos, Numerical solution of ordinary differential equations with periodical solution, Doctoral Dissertation, National Technical University of Athens, Greece, 1990 (in Greek).
    • (1990)
    • Simos, T.E.1
  • 22
    • 84987141698 scopus 로고
    • Predictor-corrector phase-fitted methods for y″=f(x,y) and an application to the Schrödinger equation
    • T.E. Simos Predictor-corrector phase-fitted methods for y″=f(x,y) and an application to the Schrödinger equation Internat. J. Quantum Chem. 53 1995 473-483
    • (1995) Internat. J. Quantum Chem. , vol.53 , pp. 473-483
    • Simos, T.E.1
  • 23
    • 0032380346 scopus 로고    scopus 로고
    • An eighth order exponentially-fitted method for the numerical solution of the Schrödinger equation
    • T.E. Simos An eighth order exponentially-fitted method for the numerical solution of the Schrödinger equation Internat. J. Modern Phys. C 9 1998 271-288
    • (1998) Internat. J. Modern Phys. C , vol.9 , pp. 271-288
    • Simos, T.E.1
  • 25
    • 0035562245 scopus 로고    scopus 로고
    • On the construction of efficient methods for second order IVPs with oscillating solution
    • T.E. Simos J. Vigo-Aguiar On the construction of efficient methods for second order IVPs with oscillating solution Internat. J. Modern Phys. C 10 2001 1453-1476
    • (2001) Internat. J. Modern Phys. C , vol.10 , pp. 1453-1476
    • Simos, T.E.1    Vigo-Aguiar, J.2
  • 26
    • 0031357296 scopus 로고    scopus 로고
    • A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation
    • R.M. Thomas T.E. Simos A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation J. Comput. Appl. Math. 87 1997 215-226
    • (1997) J. Comput. Appl. Math. , vol.87 , pp. 215-226
    • Thomas, R.M.1    Simos, T.E.2
  • 27
    • 0004958010 scopus 로고
    • Properties and implementation of r-Adams methods based on mixed-type interpolation
    • M. Van Daele G. Vanden Berghe H. De Meyer Properties and implementation of r-Adams methods based on mixed-type interpolation Comput. Math. Appl. 30 1995 37-54
    • (1995) Comput. Math. Appl. , vol.30 , pp. 37-54
    • Van Daele, M.1    Vanden Berghe, G.2    De Meyer, H.3
  • 28
    • 0038483867 scopus 로고
    • Mathematical methods for the numerical propagation of satellite orbits
    • Doctoral Dissertation, University of Valladolid, Spain (in Spanish)
    • J. Vigo-Aguiar, Mathematical methods for the numerical propagation of satellite orbits, Doctoral Dissertation, University of Valladolid, Spain, 1993 (in Spanish).
    • (1993)
    • Vigo-Aguiar, J.1
  • 29
    • 0347357926 scopus 로고    scopus 로고
    • A general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems
    • J. Vigo-Aguiar J.M. Ferrandiz A general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems SIAM J. Numer. Anal. 35 1998 1684-1708
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1684-1708
    • Vigo-Aguiar, J.1    Ferrandiz, J.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.