A Dissipative Exponentially-Fitted Method for the Numerical Solution of the Schrödinger Equation

2001 ◽  
Vol 41 (4) ◽  
pp. 909-917
Author(s):  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method

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.

STABILIZATION OF A FOUR-STEP EXPONENTIALLY-FITTED METHOD AND ITS APPLICATION TO THE SCHRÖDINGER EQUATION

2007 ◽  
Vol 18 (03) ◽  
pp. 315-328 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Linear Combination ◽  
Schrodinger Equation ◽  
Resonance Problem ◽  
Step Method ◽  
Numerical Experimentation ◽  
Radial Schrödinger Equation ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method

In this paper we present a singularly P-stable exponentially — fitted four-step method for the numerical solution of the radial Schrödinger equation. More specifically we present a method that is singularly P-stable (a concept later introduced in this paper) and also integrates exactly any linear combination of the functions {1, x, x2, x3, x4, x5, exp (±Ivx)}. The numerical experimentation showed that our method is considerably more efficient compared to well-known methods used for the numerical solution of resonance problem of the radial Schrödinger equation.

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