An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems

2000 ◽  
Vol 131 (1-2) ◽  
pp. 52-67 ◽  
Author(s):  
G. Avdelas ◽  
T.E. Simos ◽  
J. Vigo-Aguiar
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Initial Value Problems ◽  
Schrodinger Equation ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Periodic Initial Value Problems ◽  
Exponentially Fitted ◽  
Runge Kutta

scholarly journals A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yanwei Zhang ◽  
Haitao Che ◽  
Yonglei Fang ◽  
Xiong You
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Recent Literature ◽  
New Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Radial Schrödinger Equation ◽  
Runge Kutta ◽  
Fifth Order

A new trigonometrically fitted fifth-order two-derivative Runge-Kutta method with variable nodes is developed for the numerical solution of the radial Schrödinger equation and related oscillatory problems. Linear stability and phase properties of the new method are examined. Numerical results are reported to show the robustness and competence of the new method compared with some highly efficient methods in the recent literature.

AN EMBEDDED RUNGE–KUTTA METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

2000 ◽  
Vol 11 (06) ◽  
pp. 1115-1133 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Phase Lag ◽  
Kutta Method ◽  
New Methods ◽  
Runge Kutta Method ◽  
Radial Schrödinger Equation ◽  
Runge Kutta

An embedded Runge–Kutta method with phase-lag of order infinity for the numerical integration of Schrödinger equation is developed in this paper. The methods of the embedded scheme have algebraic orders five and four. Theoretical and numerical results obtained for radial Schrödinger equation and for coupled differential equations show the efficiency of the new methods.

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