Optimized Runge-Kutta pairs for problems with oscillating solutions

Journal of Computational and Applied Mathematics

Volumn 147, Issue 2, 2002, Pages 397-409

  Tsitouras, Ch ^a   Simos, T E ^b,c  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^c NONE   (Greece)

Author keywords

Dissipation; Initial value problem; Numerical solution; Phase lag; Variable step

Indexed keywords

INITIAL VALUE PROBLEMS; INTEGRATION; OPTIMIZATION; POLES AND ZEROS; RUNGE KUTTA METHODS;

OSCILLATING PROBLEMS;

COMPUTATIONAL METHODS;

MATHEMATICAL METHOD;

EID: 0037109217     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00475-2     Document Type: Article

References (22)

1. A family of embedded Runge-Kutta formulae
2. Numerical methods for differential equations based on trigonometric polynomials
3. Runge-Kutta pairs for periodic initial value problems
4. A family of fifth order Runge-Kutta pairs
5. High phase-lag order Runge-Kutta and Nyström pairs
6. A general family of explicit Runge-Kutta pairs of orders
7. A four-step phase-fitted method for the numerical integration of second order initial-value problems
8. An exponentially fitted Runge-Kutta method for the numerical integration of initial value problems with periodic or oscillating solutions
9. A P-stable eighth order method for the numerical integration of periodic initial value problems
10. A parameter study of explicit Runge-Kutta pairs of orders
11. High order zero dissipative Runge-Kutta-Nyström methods
12. High algebraic order, high dissipation order Runge-Kutta methods
13. Cheap error estimation for Runge-Kutta pairs
14. High order explicit methods for the integration of periodic initial value problems
15. Exponentially-fitted explicit Runge-Kutta methods
16. Explicit Runge-Kutta ( - Nystrom) methods with reduced phase-errors for computing oscillating solutions
17. Stabilization of Cowell's classical finite difference methods for numerical integration
18. Mathematica