Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-010-9728-9 ◽

2010 ◽

Vol 48 (4) ◽

pp. 1092-1143 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Phase Lag ◽

Second Derivatives

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A Runge–Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-013-0301-1 ◽

2013 ◽

Vol 52 (3) ◽

pp. 917-947 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Second Derivatives ◽

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A family of embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation: development and theoretical analysis

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0611-1 ◽

2016 ◽

Vol 54 (5) ◽

pp. 1159-1186 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Theoretical Analysis ◽

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

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A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0545-z ◽

2015 ◽

Vol 53 (10) ◽

pp. 2191-2213 ◽

Author(s):

Fei Hui ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Phase Lag ◽

Two Stage ◽

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Some new Numerov-type methods with minimal phase lag for the numerical integration of the radial Schrödinger equation

Molecular Physics ◽

10.1080/00268979400101841 ◽

1994 ◽

Vol 83 (6) ◽

pp. 1145-1153 ◽

Author(s):

T.E. Simos ◽

G. Mousadis

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Phase Lag ◽

Radial Schrödinger Equation ◽

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New P-stable high-order methods with minimal phase-lag for the numerical integration of the radial Schrödinger equation

Physica Scripta ◽

10.1088/0031-8949/55/6/002 ◽

1997 ◽

Vol 55 (6) ◽

pp. 644-650 ◽

Author(s):

T E Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Phase Lag ◽

High Order Methods ◽

Radial Schrödinger Equation ◽

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A new high algebraic order four stages symmetric two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0627-6 ◽

2016 ◽

Vol 54 (7) ◽

pp. 1417-1439 ◽

Author(s):

Xiaopeng Xi ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Second Derivatives ◽

Algebraic Order ◽

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New 8-step symmetric embedded predictor–corrector (EPCM) method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-018-0915-4 ◽

2018 ◽

Vol 56 (9) ◽

pp. 2741-2767 ◽

Author(s):

P. I. Stasinos ◽

Theodore E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Phase Lag ◽

First Derivative ◽

Predictor Corrector

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Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0522-6 ◽

2015 ◽

Vol 53 (8) ◽

pp. 1808-1834 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Computational Cost ◽

Phase Lag ◽

Step Method ◽

Low Computational Cost

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A new two stages tenth algebraic order symmetric six-step method with vanished phase-lag and its first and second derivatives for the solution of the radial Schrödinger equation and related problems

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0674-z ◽

2016 ◽

Vol 55 (1) ◽

pp. 105-131 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Second Derivatives ◽

Radial Schrödinger Equation ◽

Algebraic Order ◽

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New embedded explicit methods with minimal phase-lag for the numerical integration of the Schrödinger equation

Computers & Chemistry ◽

10.1016/s0097-8485(98)00003-5 ◽

1998 ◽

Vol 22 (5) ◽

pp. 433-440 ◽

Author(s):

T.E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Explicit Methods ◽

Phase Lag ◽

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