New second-order exponentially and trigonometrically fitted symplectic integrators for the numerical solution of the time-independent schrödinger equation

Journal of Mathematical Chemistry

Volumn 42, Issue 3, 2007, Pages 535-545

  Monovasilis, Th ^a   Simos, T E ^a  

^a UNIVERSITY OF PELOPONNESE   (Greece)

Author keywords

Exponential fitting; Hamiltonian canonical equation; Schr dinger equation; Symplectic Integrators; Trigonometric fitting

Indexed keywords

EID: 34548440749     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-006-9129-2     Document Type: Article

References (23)

1. Sakas D.P., Simos T.E. (2005) A family of multiderivative methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 37(3): 317-332
2. Psihoyios G., Simos T.E. (2005) Sixth algebraic order trigonometrically fitted predictor corrector methods for the numerical solution of the radial Schrödinger equation. J. Math. Chem. 37(3): 295-316
3. Anastassi Z.A., Simos T.E. (2005) Trigonometrically fitted Runge Kutta methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 37(3): 281-293
4. Avdelas G., Simos T.E. (1999) Embedded eighth order methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 26(4): 327-341
5. Simos T.E. (1999) A family of P-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 25(1): 65-84
6. Simos T.E. (2004) Exponentially-Fitted multiderivative methods for the numerical solution of the schrödinger equation. J. Math. Chem. 36(1): 13-27
7. Tselios K., Simos T.E. (2004) Symplectic methods of fifth-order for the numerical solution of the radial shrödinger equation. J. Math. Chem. 35(1): 55-63
8. Avdelas G., Kefalidis E., Simos T.E. (2002) New P-Stable eighth algebraic order exponentially-fitted methods for the numerical integration of the schrödinger equation. J. Math. Chem. 31(4): 371-404
9. Avdelas G., Konguetsof A., Simos T.E. (2001) A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the schrödinger equation. Part 1. Development of the Basic Method. J. Math. Chem. 29(4): 281-291
10. Avdelas G., Konguetsof A., Simos T.E. (2001) A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the schrödinger equation. Part 2. development of the generator, optimization of the generator and numerical results. J. Math. Chem. 29(4): 293-305
11. Simos T.E. (2000) A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation. J. Math. Chem. 27(4): 343-356
12. Arnold V. (1978). Mathematical Methods of Classical Mechanics. Springer-Verlag, Berlin
13. Psihoyios G., Simos T.E. (2004) Effective Numerical Approximation of Schrödinger type Equations through Multiderivative Exponentially fitted schemes. Appl. Num. Anal. Comp. Math. 1(1): 205-215
14. Simos T.E. (2002), Numerical methods for 1D, 2D and 3D differential equations arising in chemical problems. Chem. Model. Appl. and Theory, R. Soc. Chem. 2: 170-270
15. Simos T.E. (2005), P-stable Four-Step Exponentially-Fitted Method for the Numerical Integration of the Schrödinger Equation. Compu. Lett. 1(1): 37-45
16. Vanden Berghe G., Van Daele M., Vande Vyver H. (2004) Exponentially-fitted algorithms: fixed or frequency dependent knot points?. Appl. Num. Anal. Comp. Math. 1(1): 49-65
17. Psihoyios G., Simos T.E. (2004) Efficient Numerical Solution of Orbital Problems with the use of Symmetric Four-step Trigonometrically-fitted Methods. Appl. Num. Anal. Comp. Math. 1(1): 216-222
18. Yoshida H. (1990) Construction of higher order symplectic integrators. Phys. Lett A 150: 262-268
19. Forest E., Ruth R.D. (1990), fourth-order symplectic integration. Physica D 43: 105-117
20. Ruth R.D. (1983) A canonical integration technique. IEEE Transact. Nuclear Sci. NS 30: 2669-2671
21. Liu X.S., Liu X.Y., Zhou Z.Y., Ding P.Z., Pan S.F. (2000) Numerical solution of the one-dimensional time-independent schrödinger equation by using symplectic schemes. Int. J. Quant. Chem. 79: 343-349
22. Skorupski A.A., Infeld E. (2005) Eigenvalue problem for a set of coupled Schrödinger like ODEs. Appl. Num. Anal. Comp. Math. 2(1): 167-174
23. McLachlan R., Atela P. (1992) The accuracy of symplectic integrators. Nonlinearity 5: 541-562