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
doaj +1 more source
Parallelization of Runge–Kutta Methods for Hardware Implementation
Computation, 2022 Parallel numerical integration is a valuable tool used in many applications requiring high-performance numerical solvers, which is of great interest nowadays due to the increasing difficulty and complexity in differential problems.
Petr Fedoseev +4 more
doaj +1 more source
Numerical Simulation of Fuzzy Volterra Integro-differential Equation using Improved Runge-Kutta Method [PDF]
Journal of Applied and Computational Mechanics, 2023 In this research, fourth-order Improved Runge-Kutta method with three stages for solving fuzzy Volterra integro-differential (FVID) equations of the second kind under the concept of generalized Hukuhara differentiability is proposed. The advantage of the
Faranak Rabiei +6 more
doaj +1 more source
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
semanticscholar +1 more source
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
doaj +1 more source
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
doaj +1 more source
ANALYSIS OF THE SPRUCE BUDWORM MODEL USING THE HEUN METHOD AND THIRD-ORDER RUNGE-KUTTA
Barekeng, 2022 This study discusses the analysis of the Spruce Budworm model using numerical methods, namely the Heun method and the Third Order Runge-Kutta method. The purpose of this study is to determine the numerical results of the Heun method and the Third Order ...
Irwan Irwan +4 more
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source