Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution

Applied Mathematics Letters

Volumn 17, Issue 5, 2004, Pages 601-607

  Simos, T E ^a,b  

^a UNIVERSITY OF PELOPONNESE   (Greece)

^b NONE   (Greece)

Author keywords

Dissipative methods; Explicit methods, Hybrid methods; Initial value problems (IVPs); Multistep methods; Numerical solution; Trigonometrical fitting

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUMERICAL METHODS; PROBLEM SOLVING;

DISSIPATIVE METHODS; EXPLICIT METHODS; HYBRID METHODS; MULTISTEP METHODS; TRIGONOMETRICAL FITTING;

INITIAL VALUE PROBLEMS;

EID: 2442647571     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(04)90133-4     Document Type: Article

References (14)

1. Ch. Tsitouras, Explicit two-step methods for second-order linear IVPs, Computers Math. Applic. 43 (8/9), 943-949, (2002).
2. I. Prigogine and S. Rice, Editors, Advances in Chemical Physics, Volume 93: New Methods in Computational Quantum Mechanics, John Wiley & Sons, (1997).
3. T.E. Simos, Atomic structure computations, In Chemical Modelling: Applications and Theory, Volume 1, (Edited by A. Hinchliffe, UMIST), pp. 38-142, The Royal Society of Chemistry, (2000).
4. T.E. Simos, Numerical methods for the solution of ID, 2D and 3D differential equations arising in chemical problems, In Chemical Modelling: Applications and Theory, Volume 8, (Edited by A. Hinchliffe, UMIST), pp. 170-270, The Royal Society of Chemistry, (2002).
5. T.E. Simos and P.S. Williams, On finite difference methods for the solution of the Schrödinger equation, Computers & Chemistry 23, 513-554, (1999).
6. T.E. Simos, Numerical solution of ordinary differential equations with periodical solution, (in Greek), Doctoral Dissertation, National Technical University of Athens, Greece, (1990).
7. L.Gr. Ixaru, Numerical Methods for Differential Equations and Applications, Reidel, Dordrecht, (1984).
8. T. Lyche, Chebyshevian multistep methods for ordinary differential equations, Numerische Mathematik 10, 65-75, (1972).
9. A.D. Raptis and A.C. Allison, Exponential-fitting methods for the numerical solution of the Schrödinger equation, Computer Physics Communications 14, 1-5, (1978).
10. J.M. Franco and M. Palacios, High-order P-stable multistep methods, J. Comput. Appl. Math. 30, 1-10, (1990).
11. E. Stiefel and D.G. Bettis, Stabilization of Cowell's method, Numerische Mathematik 13, 154-175, (1969).
12. M.M. Chawla, Numerov made explicit has better stability, BIT 24, 117-118, (1984).
13. M.M. Chawla and P.S. Rao, An explicit sixth-order method with phase-lag of order eight for y″ = f(t, y), Journal of Computational and Applied Mathematics 17, 365-368, (1987).
14. J.R. Dormand, M.E.A. El-Mikkawy and P.J. Prince, High-order embedded Runge-Kutt-Nyström formulae, IMA Journal of Numerical Analysis 7, 423-430, (1987).