منابع مشابه
Energy-preserving Runge-kutta Methods
We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are the energy invariant of canonical Hamiltonian systems. Mathematics Subject Classification. 65P10, 65L06. Received May 21, 2008. Published online July 8, 2009. All Runge-Kutta (RK) methods preserve arbitrary linear invariants [12], and some (the symplectic) RK methods p...
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In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious o...
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We study Runge{Kutta methods for the integration of ordinary diierential equations and their retention of algebraic invariants. As a general rule, we derive two conditions for the retention of such invariants. The rst is a condition on the co-eecients of the methods, the second is a pair of partial diierential equations that otherwise must be obeyed by the invariant. The cases related to the re...
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Exponential Runge-Kutta (ERK) and partitioned exponential Runge-Kutta (PERK) 4 methods are developed for solving initial value problems with vector fields that can be split into con5 servative and linear non-conservative parts. The focus is on linearly damped ordinary differential 6 equations, that possess certain invariants when the damping coefficient is zero, but, in the presence of 7 consta...
متن کامل2-stage explicit total variation diminishing preserving runge-kutta methods
in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...
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ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2009
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2009020