Algebraic Order for Some Exponentially–Fitted Explicit Runge–Kutta Methods

2003 ◽  
Vol 3 (1) ◽  
pp. 55-71
Author(s):  
J.M. Franco
Keyword(s):  
Algebraic Order ◽  
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 TWO-DERIVATIVE RUNGE–KUTTA METHODS FOR THE SCHRÖDINGER EQUATION

2013 ◽  
Vol 24 (10) ◽  
pp. 1350073 ◽  
Author(s):  
YONGLEI FANG ◽  
XIONG YOU ◽  
QINGHE MING
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
High Efficiency ◽  
New Methods ◽  
Asymptotic Expressions ◽  
Radial Schrödinger Equation ◽  
Algebraic Order ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
Order Four

Two exponentially fitted two-derivative Runge–Kutta (EFTDRK) methods of algebraic order four are derived. The asymptotic expressions of the local errors for large energies are obtained. The numerical results in the integration of the radial Schrödinger equation with the Woods–Saxon potential show the high efficiency of our new methods compared to some famous optimized codes in the literature.

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.

Exponentially fitted symplectic Runge-Kutta-Nyström methods

2012 ◽  
Author(s):  
Th. Monovasilis ◽  
Z. Kalogiratou ◽  
T. E. Simos
Keyword(s):  
Exponentially Fitted ◽  
Runge Kutta

scholarly journals Three-Stage Two-Parameter Symplectic, Symmetric Exponentially-Fitted Runge-Kutta Methods of Gauss Type

2010 ◽  
Author(s):  
M. Van Daele ◽  
D. Hollevoet ◽  
G. Vanden Berghe ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Gauss Type ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
Two Parameter
Sign in / Sign up

Export Citation Format

Share Document