High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

Ibraheem Alolyan; T. E. Simos

doi:10.1007/s10910-010-9718-y

High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-010-9718-y ◽

2010 ◽

Vol 48 (4) ◽

pp. 925-958 ◽

Cited By ~ 34

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

First Derivative ◽

Algebraic Order

A family of high algebraic order embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation and related problems

10.1063/1.4968772 ◽

2016 ◽

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Algebraic Order

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

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0654-3 ◽

2016 ◽

Vol 54 (9) ◽

pp. 1835-1862 ◽

Cited By ~ 15

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Radial Schrödinger Equation ◽

Algebraic Order ◽

Two Stages

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 ◽

Cited By ~ 34

Author(s):

Xiaopeng Xi ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Second Derivatives ◽

Algebraic Order ◽

Order Four

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 ◽

Cited By ~ 47

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Algebraic Order

A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-011-9862-z ◽

2011 ◽

Vol 49 (9) ◽

pp. 1843-1888 ◽

Cited By ~ 11

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

First Derivative

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 ◽

Cited By ~ 13

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Step Method ◽

Algebraic Order

Runge-Kutta Type Tenth Algebraic Order Method with Vanished Phase-Lag and its First, Second, Third, Fourth and Fifth Derivatives for the Numerical Solution of the Schrodinger Equation

Applied Mathematics & Information Sciences ◽

10.18576/amis/100114 ◽

2016 ◽

Vol 10 (1) ◽

pp. 143-153 ◽

Cited By ~ 1

Author(s):

Fei Hui ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Order Method ◽

Algebraic Order ◽

Runge Kutta

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 ◽

Cited By ~ 66

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 ◽

Runge Kutta

Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2004.06.013 ◽

2005 ◽

Vol 175 (1) ◽

pp. 161-172 ◽

Cited By ~ 127

Author(s):

D.P. Sakas ◽

T.E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Radial Schrödinger Equation ◽

Algebraic Order ◽

Minimal Phase ◽

Multiderivative Methods

A high algebraic order predictor–corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problems

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0502-x ◽

2015 ◽

Vol 53 (7) ◽

pp. 1495-1522 ◽

Cited By ~ 47

Author(s):

Ibraheem Alolyan ◽

T. E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

Phase Lag ◽

Explicit Method ◽

Algebraic Order ◽

Predictor Corrector