Results 11 to 20 of about 32,424,344 (291)
SIAM Journal on Scientific Computing, 2019 The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms}, SIAM Journal on Numerical Analysis, 2019) is extended to general
Dalcin, Lisandro +4 more
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Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models [PDF]
Geoscientific Model Development, 2018 The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves.
D. J. Gardner +5 more
doaj +2 more sources
Implicit and Implicit-Explicit Strong Stability Preserving Runge-Kutta Methods with High Linear Order [PDF]
Journal of Scientific Computing, 2017 When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity properties satisfied by
Conde, Sidafa +3 more
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Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation [PDF]
Applied Mathematics Letters, 2020 In this paper, a family of arbitrarily high-order structure-preserving exponential Runge–Kutta methods are developed for the nonlinear Schrodinger equation by combining the scalar auxiliary variable approach with the exponential Runge–Kutta method.
Jin Cui +3 more
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Fractional Order Runge-Kutta Methods [PDF]
Fractal and Fractional, 2022 This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution of fractional differential equations (FDEs).
F. Ghoreishi, Rezvan Ghaffari
semanticscholar +1 more source
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations [PDF]
Journal of Computational Physics, 2020 A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions.
L. Ju +3 more
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Relaxation Runge–Kutta Methods for Hamiltonian Problems [PDF]
Journal of Scientific Computing, 2020 The recently-introduced relaxation approach for Runge–Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge–Kutta methods in this context. We
Hendrik Ranocha, D. Ketcheson
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Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms [PDF]
SIAM Journal on Numerical Analysis, 2019 We further develop a simple modification of Runge--Kutta methods that guarantees conservation or stability with respect to any inner-product norm. The modified methods can be explicit and retain the accuracy and stability properties of the unmodified ...
D. Ketcheson
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Conservative Continuous-Stage Stochastic Runge–Kutta Methods for Stochastic Differential Equations
Fractal and Fractional, 2023 In this paper, we develop a new class of conservative continuous-stage stochastic Runge–Kutta methods for solving stochastic differential equations with a conserved quantity. The order conditions of the continuous-stage stochastic Runge–Kutta methods are
Xiuyan Li +3 more
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Construction of Two-Derivative Runge–Kutta Methods of Order Six
Algorithms, 2023 Two-Derivative Runge–Kutta methods have been proposed by Chan and Tsai in 2010 and order conditions up to the fifth order are given. In this work, for the first time, we derive order conditions for order six.
Zacharoula Kalogiratou +1 more
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