Results 11 to 20 of about 11,954,701 (266)
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
doaj +4 more sources
Practical symplectic partitioned Runge–Kutta and Runge–Kutta–Nyström methods [PDF]
Journal of Computational and Applied Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Blanes, S., Moan, P. C.
openaire +3 more sources
Quadratic projectable Runge–Kutta methods
Communications of the American Mathematical SocietyRunge–Kutta methods are affine equivariant: applying a method before or after an affine change of variables yields the same numerical trajectory. However, for some applications, one would like to perform numerical integration after a quadratic change of variables.
Ari Stern, Milo Viviani
openaire +3 more sources
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
openaire +4 more sources
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
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source