A trigonometrically-fitted one-step method with multi-derivative for the numerical solution to the one-dimensional Schrödinger equation

2005 ◽  
Vol 170 (1) ◽  
pp. 49-64 ◽  
Author(s):  
Zhongcheng Wang ◽  
Qimang Chen
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Step Method ◽  
One Dimensional ◽  
One Step ◽  
The One

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.

AN ACCURATE EXPONENTIALLY FITTED EXPLICIT FOUR-STEP METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION

1998 ◽  
Vol 13 (15) ◽  
pp. 2613-2626 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Exponential Functions ◽  
Step Method ◽  
One Dimensional ◽  
Radial Schrödinger Equation ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method ◽  
Free Parameters ◽  
The One

We present here an accurate exponentially fitted explicit four-step method for the numerical integration of the one-dimensional Schrödinger equation. The formula considered contains free parameters which are defined in order to integrate exponential functions. We note that this is the first explicit four-step exponentially fitted method in the literature. Numerical results also indicate that the new method is much more accurate than other well-known methods.

Sign in / Sign up

Export Citation Format

Share Document