A Runge–Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equation

2013 ◽  
Vol 52 (3) ◽  
pp. 917-947 ◽  
Author(s):  
Ibraheem Alolyan ◽  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Phase Lag ◽  
Step Method ◽  
Second Derivatives ◽  
Runge Kutta

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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