An exponentially fitted method for solving Burgers' equation

2009 ◽  
Vol 79 (6) ◽  
pp. 696-705 ◽  
Author(s):  
Turgut Öziş ◽  
Utku Erdoğkan
Keyword(s):  
Burgers Equation ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method

P-stable Four-Step Exponentially-Fitted Method for the Numerical Integration of the Schr¨odinger Equation

2004 ◽  
Vol 1 (1) ◽  
pp. 37-44 ◽  
Author(s):  
T.E. Simos
Keyword(s):  
Numerical Solution ◽  
Linear Combination ◽  
Numerical Integration ◽  
Resonance Problem ◽  
Step Method ◽  
Numerical Experimentation ◽  
Exponentially Fitted ◽  
Exponentially Fitted Method

In this paper we present a P-stable exponentially-fitted four-step method for the numerical solution of the radial Schr¨odinger equation. More specifically we present a method than satisfies the property of P-stability and in the same time integrates exactly any linear combination of the functions {1, x, x2, x3, exp ± w x , x exp ± w x}. We tested the efficiency of our newly obtained scheme against well known methods, with excellent results. 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 Schr¨odinger equation.

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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