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A new family of A-stable Runge-Kutta methods with equation-dependent (EDRK) coefficients for the numerical solution of stiff differential equations is investigated. The newly constructed four-stage EDRK methods are of algebraic order five. The linear stability properties are analyzed. Numerical experiments are carried out to show the efficiency of the new methods compared with the existing codes in...
In this paper the order conditions for Runge-Kutta (RK) methods are presented based on Butcher's B-series theory. New concepts of internal orders vector and stage orders of RK methods are proposed. The internal and stage orders of some classical RK methods are examined. Two new methods with improved internal orders are constructed. The results of numerical experiments show the competence of the new...
In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.
The Lotka-Volterra system is traditionally integrated with the classical Runge-Kutta method of order four or the Runge-Kutta-Fehlberg method which fails to preserve the special structure of the system in long term integration. This paper transforms the Lotka-Volterra system into a Hamiltonian system and integrates it with two highly efficient symplectic methods. The results of the numerical simulation...
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