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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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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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Solving Oscillating Problems Using Modifying Runge-Kutta Methods
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2021 This paper develop conventional Runge-Kutta methods of order four and order five to solve ordinary differential equations with oscillating solutions.
Zainab Khaled Ghazal +1 more
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Optimum Runge-Kutta methods [PDF]
Mathematics of Computation, 1964 The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size of the truncation error are considered. The optimum method is practically independent of the measure being used. Moreover, among methods of the same order which one might consider using the difference in size of the ...
Hull, T. E., Johnston, R. L.
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Different approaches in GLONASS orbit computation from broadcast ephemeris [PDF]
Geodetski Vestnik, 2016 Several types of methods can solve equations of satellite motion numerically. These methods are divided into single and multi-step methods. The accuracy of each method depends directly on adopted integration step size between successive iterations.
Kamil Maciuk
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Improved Runge-Kutta Method for Oscillatory Problem Solution Using Trigonometric Fitting Approach
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023 This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an oscillatory character in the solutions.
Kasim A. Hussain, Waleed J. Hasan
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Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations
Journal of Nigerian Society of Physical Sciences, 2020 Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are ...
M. O. Ogunniran +3 more
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Stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential algebraic equations
Results in Applied Mathematics, 2021 In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge–Kutta methods for finding the numerical approximate solutions to multi-dimensional ...
Priya Nair, Anandaraman Rathinasamy
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Extrapolated Implicit–Explicit Runge–Kutta Methods
Mathematical Modelling and Analysis, 2014 We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by
Angelamaria Cardone +3 more
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Runge-Kutta methods are stable
CoRR, 2023 We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong stability, fail to secure the stability of arbitrarily large RK systems.
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