EXPONENTIAL-FITTING SYMPLECTIC METHODS FOR THE NUMERICAL INTEGRATION OF THE SCHRÖDINGER EQUATION

2003 ◽  
Author(s):  
TH. MONOVASILIS ◽  
Z. KALOGIRATOU ◽  
T.E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Exponential Fitting ◽  
Symplectic Methods

TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS

2011 ◽  
Vol 22 (12) ◽  
pp. 1343-1355 ◽  
Author(s):  
TH. MONOVASILIS ◽  
Z. KALOGIRATOU ◽  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Phase Lag ◽  
Symplectic Methods ◽  
Hamiltonian Problems ◽  
Algebraic Order ◽  
Runge Kutta ◽  
New Phase

New symplectic Partitioned Runge–Kutta (SPRK) methods with phase-lag of order infinity are derived in this paper. Specifically two new symplectic methods are constructed with second and third algebraic order. The methods are tested on the numerical integration of Hamiltonian problems and on the estimation of the eigenvalues of the Schrödinger equation.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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