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

2005 ◽  
Vol 175 (1) ◽  
pp. 161-172 ◽  
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 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.

A SYMMETRIC HIGH ORDER METHOD WITH MINIMAL PHASE-LAG FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

2001 ◽  
Vol 12 (07) ◽  
pp. 1035-1042 ◽  
Author(s):  
T. E. SIMOS ◽  
JESUS VIGO AGUIAR
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Method ◽  
Phase Lag ◽  
Step Method ◽  
High Order Method ◽  
Radial Schrödinger Equation ◽  
Algebraic Order ◽  
Minimal Phase ◽  
Symmetric Method

In this paper, a new high algebraic order symmetric eight-step method is introduced. For this method, a direct formula for the computation of the phase-lag is given. Based on this formula, an eight-step symmetric method with minimal phase-lag is developed. The new method has better stability properties than the classical one. Numerical illustrations on the radial Schrödinger equation indicate that the new method is more efficient than older ones.

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.

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