A four-step exponentially fitted method for the numerical solution of the Schrödinger equation

[1]  Z. Kalogiratou,et al.  Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation , 2006 .

[2]  T. E. Simos,et al.  A P-stable exponentially-fitted method for the numerical integration of the Schrödinger equation , 2005 .

[3]  Zacharoula Kalogiratou,et al.  Trigonometrically and Exponentially fitted Symplectic Methods of third order for the Numerical Integration of the Schrödinger Equation , 2005 .

[4]  D. P. Sakas,et al.  A family of multiderivative methods for the numerical solution of the Schrödinger equation , 2005 .

[5]  G. Vanden Berghe,et al.  Extended One‐Step Methods: An Exponential Fitting Approach , 2004 .

[6]  D. S. Vlachos,et al.  Partitioned Linear Multistep Method for Long Term Integration of the N‐Body Problem , 2004 .

[7]  E. Aydiner.  The Time Evaluation of Resistance Probability of a Closed Community against Occupation in a Sznajd-Like Model with Synchronous Updating: , 2004, cond-mat/0405490.

[8]  T. E. Simos,et al.  Exponentially - Fitted Multiderivative Methods for the Numerical Solution of the Schrödinger Equation , 2004 .

[9]  G. Psihoyios,et al.  Efficient Numerical Solution of Orbital Problems with the use of Symmetric Four-step Trigonometrically-fitted Methods , 2004 .

[10]  Georgios Psihoyios,et al.  Effective Numerical Approximation of Schrödinger type Equations through Multiderivative Exponentially‐fitted Schemes , 2004 .

[11]  G. Vanden Berghe,et al.  Exponentially-fitted algorithms: fixed or frequency dependent knot points? , 2004 .

[12]  Z. Kalogiratou,et al.  Numerical Solution of the two-dimensional time independent Schrödinger Equation by symplectic schemes† , 2004 .

[13]  K. Tselios,et al.  Symplectic Methods for the Numerical Solution of the Radial Shrödinger Equation , 2003 .

[14]  T. E. Simos,et al.  A Family of Trigonometrically-Fitted Symmetric Methods for the Efficient Solution of the Schrödinger Equation and Related Problems , 2003 .

[15]  T. E. Simos,et al.  Family of Twelve Steps Exponential Fitting Symmetric Multistep Methods for the Numerical Solution of the Schrödinger Equation , 2002 .

[16]  T. E. Simos,et al.  Numerical methods for the solution of 1D, 2D and 3D differential equations arising in chemical problems , 2002 .

[17]  T. E. Simos,et al.  New P-Stable Eighth Algebraic Order Exponentially-Fitted Methods for the Numerical Integration of the Schrödinger Equation , 2002 .

[18]  Zacharoula Kalogiratou,et al.  Construction of Trigonometrically and Exponentially Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of the Schrödinger Equation and Related Problems – a Method of 8th Algebraic Order , 2002 .

[19]  T. E. Simos,et al.  Symmetric Eighth Algebraic Order Methods with Minimal Phase-Lag for the Numerical Solution of the Schrödinger Equation , 2002 .

[20]  Tom E. Simos,et al.  A Modified Phase-Fitted Runge–Kutta Method for the Numerical Solution of the Schrödinger Equation , 2001 .

[21]  G. Avdelas,et al.  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 , 2001 .

[22]  Theodore E. Simos,et al.  A Modified Runge-Kutta Method with Phase-lag of Order Infinity for the Numerical Solution of the Schrödinger Equation and Related Problems , 2001, Comput. Chem..

[23]  G. Avdelas,et al.  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 , 2001 .

[24]  T. E. Simos,et al.  A Family of P-stable Eighth Algebraic Order Methods with Exponential Fitting Facilities , 2001 .

[25]  T. E. Simos,et al.  Atomic structure computations , 2000 .

[26]  T. Simos.  A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation , 2000 .

[27]  Theodore E. Simos,et al.  On Finite Difference Methods for the Solution of the Schrödinger Equation , 1999, Comput. Chem..

[28]  G. Avdelas,et al.  Embedded eighth order methods for the numerical solution of the Schrödinger equation , 1999 .

[29]  T. E. Simos,et al.  A family of P-stable exponentially‐fitted methods for the numerical solution of the Schrödinger equation , 1999 .

[30]  T. E. Simos,et al.  A new finite-difference method with minimal phase lag for the numerical solution of differential equations with engineering applications , 1999 .

[31]  T. E. Simos,et al.  Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations , 1998 .

[32]  T. E. Simos,et al.  Eighth order methods with minimal phase‐lag for accurate computations for the elastic scattering phase‐shift problem , 1997 .

[33]  Tom E. Simos,et al.  An Eighth-Order Method With Minimal Phase-Lag For Accurate Computations For The Elastic Scattering Phase-Shift Problem , 1996 .

[34]  A. D. Raptis,et al.  A four-step phase-fitted method for the numerical integration of second order initial-value problems , 1991 .

[35]  John P. Coleman,et al.  Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine , 1989 .

[36]  Moawwad E. A. El-Mikkawy,et al.  High-Order Embedded Runge-Kutta-Nystrom Formulae , 1987 .

[37]  Moawwad E. A. El-Mikkawy,et al.  Families of Runge-Kutta-Nystrom Formulae , 1987 .

[38]  M H Chawla,et al.  A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value , 1986 .

[39]  A. D. Raptis,et al.  A variable step method for the numerical integration of the one-dimensional Schrödinger equation , 1985 .

[40]  M. M. Chawla,et al.  Numerov made explicit has better stability , 1984 .

[41]  M. Chawla.  Unconditionally stable noumerov-type methods for second order differential equations , 1983 .

[42]  A. D. Raptis,et al.  Exponentially-fitted solutions of the eigenvalue Shrödinger equation with automatic error control , 1983 .

[43]  A. D. Raptis,et al.  On the numerical solution of the Schrödinger equation , 1981 .

[44]  A. C. Allison,et al.  Exponential-fitting methods for the numerical solution of the schrodinger equation , 1978 .

[45]  J. Lambert,et al.  Symmetric Multistip Methods for Periodic Initial Value Problems , 1976 .

[46]  A. C. Allison,et al.  The numerical solution of coupled differential equations arising from the Schrödinger equation , 1970 .

[47]  John M. Blatt,et al.  Practical points concerning the solution of the Schrödinger equation , 1967 .

[48]  Alexander Dalgarno,et al.  Thermal scattering of atoms by homonuclear diatomic molecules , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[49]  P. Henrici.  Discrete Variable Methods in Ordinary Differential Equations , 1962 .

[50]  J. W. Cooley,et al.  An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields , 1961 .

[51]  Richard B. Bernstein,et al.  Quantum Mechanical (Phase Shift) Analysis of Differential Elastic Scattering of Molecular Beams , 1960 .

[52]  T. E. Simos.  P-stable Four-Step Exponentially-Fitted Method for the Numerical Integration of the Schr¨odinger Equation , 2005 .

[53]  T. Simos,et al.  On the Construction of Exponentially-Fitted Methods for the Numerical Solution of the Schrödinger Equation , 2001 .

[54]  Liviu Gr Ixaru,et al.  Numerical methods for differential equations and applications , 1984 .

[55]  M. Rizea,et al.  A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies , 1980 .

[56]  A. Messiah.  Quantum Mechanics , 1961 .

[57]  G. Herzberg,et al.  Spectra of diatomic molecules , 1950 .