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Accelerated Runge-Kutta Methods [PDF]
Discrete Dynamics in Nature and Society, 2008 Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step ...
Firdaus E. Udwadia, Artin Farahani
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Semantic Segmentation of Medical Images Based on Runge–Kutta Methods [PDF]
Bioengineering, 2023 In recent years, deep learning has achieved good results in the semantic segmentation of medical images. A typical architecture for segmentation networks is an encoder–decoder structure.
Mai Zhu, Chong Fu, Xingwei Wang
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Exponentially fitted Runge-Kutta methods [PDF]
Journal of Computational and Applied Mathematics, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
De Meyer, Hans +3 more
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Spatially partitioned embedded Runge-Kutta Methods [PDF]
SIAM Journal on Numerical Analysis, 2013 We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain.
Ketcheson, D. I. +2 more
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Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order [PDF]
The Scientific World Journal, 2014 The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented.
Y. H. Cong, C. X. Jiang
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Solving system of Euler's equations using Runge –Kutta methods [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2023 In this paper, linear systems with variable coefficients (Euler's equations) were solved using one of the numerical methods that are subject to initial conditions defined over a given period of time .The explicit Rung-Kutta method is the fastest and most
Aseel Al_Ameely, Athraa Albukhuttar
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Fractional Order Runge–Kutta Methods
Fractal and Fractional, 2023 This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution of fractional differential equations (FDEs).
Farideh Ghoreishi +2 more
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Periodica Mathematica Hungarica, 2023 AbstractIn the numerical integration of nonlinear autonomous initial value problems, the computational process depends on the step size scaled vector field hf as a distinct entity. This paper considers a parameterized transformation $$\begin{aligned} hf \mapsto hf \circ (I-\gamma hf)^{-1}, \end{aligned}$$
Molnár, András +2 more
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Krylov SSP Integrating Factor Runge–Kutta WENO Methods
Mathematics, 2021 Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF ...
Shanqin Chen
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Continuous stage stochastic Runge–Kutta methods
Advances in Difference Equations, 2021 In this work, a version of continuous stage stochastic Runge–Kutta (CSSRK) methods is developed for stochastic differential equations (SDEs). First, a general order theory of these methods is established by the theory of stochastic B-series and ...
Xuan Xin, Wendi Qin, Xiaohua Ding
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