A new hybrid 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/s10910-012-0008-8 ◽

2012 ◽

Vol 50 (7) ◽

pp. 1861-1881 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Second Derivatives

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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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A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-011-9897-1 ◽

2011 ◽

Vol 49 (10) ◽

pp. 2486-2518 ◽

Author(s):

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

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A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0571-x ◽

2015 ◽

Vol 54 (2) ◽

pp. 442-465 ◽

Author(s):

Zhou Zhou ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Two Stage ◽

Radial Schrödinger Equation

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A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0529-z ◽

2015 ◽

Vol 53 (8) ◽

pp. 1915-1942 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Algebraic Order

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Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag

Journal of Applied Mathematics ◽

10.1155/2012/420387 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Author(s):

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Oscillating Solutions ◽

Radial Schrödinger Equation

We use a methodology of optimization of the efficiency of a hybrid two-step method for the numerical solution of the radial Schrödinger equation and related problems with periodic or oscillating solutions. More specifically, we study how the vanishing of the phase-lag and its derivatives optimizes the efficiency of the hybrid two-step method.

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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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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 new eight algebraic order embedded explicit six-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0645-4 ◽

2016 ◽

Vol 54 (8) ◽

pp. 1696-1727 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Algebraic Order

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A Runge–Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0484-8 ◽

2015 ◽

Vol 53 (5) ◽

pp. 1239-1256 ◽

Author(s):

Kenan Mu ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Differential Equations ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Coupled Differential Equations ◽

Algebraic Order ◽

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New two stages high order symmetric six-step method with vanished phase–lag and its first, second and third derivatives for the numerical solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0691-y ◽

2016 ◽

Vol 55 (2) ◽

pp. 503-531 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

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