Explicit symplectic partitioned Runge-Kutta methods
2 Symmetric and Symplectic Runge-Kutta Methods
... Symmetric methods such as the implicit midpoint rule (IMR), implicit trape- zoidal rule (ITR) and 2-stage Gauss method are beneficial in solving Hamiltonian problems since they are also ...symplectic. ...
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Starting algorithms for partitioned Runge-Kutta methods: the pair Lobatto IIIA-IIIB
... In this paper we consider the Lobatto IIIA-IIIB pair. Applying the theory de- veloped by the authors for PRK methods, we obtain optimum predictors for this pair. Numerical experiments show the efficiency of these ...
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Stepsize Selection in Explicit Runge Kutta Methods for Moderately Stiff Problems
... Abstract We present an algorithm for determining the stepsize in an explicit Runge-Kutta method that is suitable when solving moderately stiff differential equations. The algorithm has a geometric ...
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Design and Analysis of Some Third Order Explicit Almost Runge Kutta Methods
... derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme; they are shown to satisfy the criteria for both consistency and stability; hence ...
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High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers
... However, in general it is not possible to employ the new introduced weights to improve the stability of high order methods. We show, for any given s-stage method with extended weights which fulfills the ...
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Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models
... the methods at any given time step, the results of the implicit–explicit simulations (HEVI or IMEX) are compared against the range of maximum vertical velocities produced by five explicit simulations ...
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2-stage explicit total variation diminishing preserving Runge-Kutta methods
... 2-stage explicit Runge-Kutta methods of order two (RK2) when ap- plied to the numerical solution of special nonlinear initial value problems (IVPs) for ...
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A Three Stage Multiderivative Explicit Runge Kutta Method
... ABSTRACT In recent years, the derivation of Runge-Kutta methods with higher derivatives has been on the increase. In this paper, we present a new class of three stage Runge-Kutta method ...
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Math 128a: Runge-Kutta Methods
... This is a much more convenient way to represent the Runge Kutta method instead of writing out all the individual k 0 s. Each of these k i ’s are what’s known as a stage derivative. We call it a derivative ...
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Preconditioning of implicit Runge-Kutta methods
... IRK methods, such as Radau IIA, Gauss, and Lobatto IIIC methods, arise as conjugate complex eigenpairs with nonzero imaginary ...IRK methods are used in a partitioned/additive way, such as for ...
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Half-Explicit Exponential Runge-Kutta Methods for Index- 1 DAEs in Helicopter Simulation
... exponential Runge-Kutta (HEERK) methods. This class of methods is very valuable in our setting, where we deal with a linear stiff part and a nonlinear nonstiff part in our DAE ...of ...
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Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
... the explicit set contains the ”largest” elements (based on length in 1D, chord of triangle or other measure of length in 2D), while the implicit set contains the “smallest” elements which are responsible for ...
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Weak second order explicit exponential Runge-Kutta methods for stochastic differential equations
... our methods to SDEs with a semilinear drift term and they have very good performance if the stiffness of the problem is in the matrix A, not in the nonlinear function f ...our methods will have a significant ...
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Implicit symmetric and symplectic exponentially fitted modified Runge–Kutta–Nyström methods for solving oscillatory problems
... But when it comes to applications, the true frequency is often unpredictable. Therefore, we need to try some different candidates. For Problems 2 and 3, we find that ISSEFMRKN2 is much more accurate and efficient than our ...
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A class of implicit symmetric symplectic and exponentially fitted Runge–Kutta–Nyström methods for solving oscillatory problems
... symmetric, symplectic, and exponentially fitted conditions has emerged. These methods show a better behavior than the other methods which do not possess these three conditions ...on explicit ...
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Implicit Runge-Kutta Methods for Orbit Propagation
... Implicit Runge-Kutta Methods for Orbit Propagation Jeffrey ...implicit Runge-Kutta- based method for orbit propagation that is superior to existing explicit methods, even ...
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On the Derivation and Implementation of a Four Stage Harmonic Explicit Runge Kutta Method*
... of Runge-Kutta methods based on averages other than the arith- metic mean is on the ...of explicit Runge-Kutta method, by introducing the harmonic mean as against the usual ...
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EXPLICIT RUNGE KUTTA METHOD IN SOLVING FUZZY INITIAL VALUE PROBLEM
... an explicit s-stage Runge-Kutta method has order p, then it can be proven that the number of stages must satisfy s p , and if p 5 , then s p 1 ...known methods of order 8 have at least ...
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Nonstandard explicit third-order Runge-Kutta method with positivity property
... Numerical methods based on finite difference approximations, Taylor series expansion, and interpolation, such as Euler, Runge-Kutta and Adams methods are widely used, ...
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On the stability function of functionally fitted Runge–Kutta methods
... For an explicit rk, A is strictly lower-triangular and c 1 = 0 , allowing to directly compute the iterates. However, for an implicit rk, A is general and so the iteration scheme is non-linear and needs special ...
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