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

2016 ◽  
Vol 54 (9) ◽  
pp. 1835-1862 ◽  
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 four-step P-stable Obrechkoff method with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation

2019 ◽  
Vol 354 ◽  
pp. 569-586 ◽  
Author(s):  
Ali Shokri ◽  
Jesús Vigo-Aguiar ◽  
Mohammad Mehdizadeh Khalsaraei ◽  
Raquel Garcia-Rubio
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Phase Lag ◽  
Radial Schrödinger Equation

High Algebraic Order Methods with Minimal Phase-Lag for Accurate Solution of the Schrödinger Equation

1998 ◽  
Vol 09 (07) ◽  
pp. 1055-1071 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Finite Difference Methods ◽  
Accurate Solution ◽  
Phase Lag ◽  
Jones Potential ◽  
Coupled Equations ◽  
Radial Schrödinger Equation ◽  
Algebraic Order ◽  
Accurate Computations

A family of new hybrid four-step tenth algebraic order methods with phase-lag of order fourteen is developed for accurate computations of the radial Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lennard-Jones potential and for the numerical solution of the coupled equations arising from the Schrödinger equation show that these new methods are better than other finite difference methods.

A NEW SYMMETRIC EIGHT-STEP PREDICTOR-CORRECTOR METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION AND RELATED ORBITAL PROBLEMS

2011 ◽  
Vol 22 (02) ◽  
pp. 133-153 ◽  
Author(s):  
G. A. PANOPOULOS ◽  
Z. A. ANASTASSI ◽  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Method ◽  
Phase Lag ◽  
Oscillating Solutions ◽  
Orbital Problems ◽  
Radial Schrödinger Equation ◽  
Algebraic Order ◽  
Predictor Corrector ◽  
Minimal Phase

A new general multistep predictor-corrector (PC) pair form is introduced for the numerical integration of second-order initial-value problems. Using this form, a new symmetric eight-step predictor-corrector method with minimal phase-lag and algebraic order ten is also constructed. The new method is based on the multistep symmetric method of Quinlan–Tremaine,1 with eight steps and 8th algebraic order and is constructed to solve numerically the radial time-independent Schrödinger equation. It can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with minimal phase-lag is the most efficient of all the compared methods and for all the problems solved.

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