Exponentially fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation and related problems

2000 ◽  
Vol 18 (3-4) ◽  
pp. 315-332 ◽  
Author(s):  
T.E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Exponentially Fitted ◽  
Runge Kutta

EXPONENTIALLY FITTED RUNGE–KUTTA FOURTH ALGEBRAIC ORDER METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS

2000 ◽  
Vol 11 (04) ◽  
pp. 785-807 ◽  
Author(s):  
P. S. WILLIAMS ◽  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Schrodinger Equation ◽  
Variable Step ◽  
Algebraic Order ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
Step Algorithm

Fourth order exponential and trigonometric fitted Runge–Kutta methods are developed in this paper. They are applied to problems involving the Schrödinger equation and to other related problems. Numerical results show the superiority of these methods over conventional fourth order Runge–Kutta methods. Based on the methods developed in this paper, a variable-step algorithm is proposed. Numerical experiments show the efficiency of the new algorithm.

EXPONENTIALLY-FITTED RUNGE–KUTTA THIRD ALGEBRAIC ORDER METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS

1999 ◽  
Vol 10 (05) ◽  
pp. 839-851 ◽  
Author(s):  
T. E. SIMOS ◽  
P. S. WILLIAMS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Results ◽  
New Methods ◽  
Algebraic Order ◽  
Exponentially Fitted ◽  
Runge Kutta

Exponentially and trigonometrically fitted third algebraic order Runge–Kutta methods for the numerical integration of the Schrödinger equation are developed in this paper. Numerical results obtained for several well known problems show the efficiency of the new methods.

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