Trigonometrically and Exponentially fitted Symplectic Methods of third order for the Numerical Integration of the Schrödinger Equation

2005 ◽  
Vol 2 (2) ◽  
pp. 238-244 ◽  
Author(s):  
Th. Monovasilis ◽  
Z. Kalogiratou ◽  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Symplectic Methods ◽  
Third Order ◽  
Exponentially Fitted

An Eighth Order Exponentially Fitted Method for the Numerical Solution of the Schrödinger Equation

1998 ◽  
Vol 09 (02) ◽  
pp. 271-288 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
New Method ◽  
Exponential Functions ◽  
Eighth Order ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method ◽  
Free Parameters

An eighth order exponentially fitted method is developed for the numerical integration of the Schrödinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. This is the first eighth order exponentially fitted method in the literature. Numerical results also indicate that the new method is much more accurate than other classical and exponentially fitted methods.

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