A Particle Swarm Runge-Kutta Optimization Algorithm for Solving the BVP of Ordinary Differential Equation

2014 ◽  
Vol 11 (1) ◽  
pp. 79-91 ◽  
Author(s):  
Lipu Zhang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimization Algorithm ◽  
Particle Swarm ◽  
Runge Kutta

Modeling on Falling Velocity of Sodiumtetraborate Aqueous Solution Drops before the Gelation of PVA-TiO2 Suspensions by the Runge-Kutta Method in Matlab 6.5

2008 ◽  
Vol 368-372 ◽  
pp. 1683-1685
Author(s):  
Cheng Long Yu ◽  
Xiu Feng Wang ◽  
Jun Xin Zhou ◽  
Hong Tao Jiang ◽  
Yan Wang
Keyword(s):  
Differential Equation ◽  
Aqueous Solution ◽  
Ordinary Differential Equation ◽  
Elevation Angle ◽  
Time Dependent ◽  
Quadratic Term ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Air Resistance ◽  
Runge Kutta

Numerical modeling on falling of sodiumtetraborate aqueous solution drops as the initiator before the gelation of PVA-TiO2 suspensions was conducted. Effect of time and elevation angle of the PVA-TiO2 suspensions on the falling velocity of the sodiumtetraborate aqueous solution drops was analyzed. An ordinary differential equation was given. Integration of the ordinary differential equation was fulfilled using the fourth-order Runge-Kutta method in Matlab 6.5. From the model, a two-order nonlinear effect of time on the velocity of the drops during falling is determined and the quadratic term -3.408t2 serves as the time dependent air resistance. The component of the falling velocity along the suspensions increases with the increasing of the elevation angle. However, for the component vertical to the suspensions, with elevation angle increasing, it decreases.

scholarly journals A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
I. B. Aiguobasimwin ◽  
R. I. Okuonghae
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Initial Value ◽  
Large Interval ◽  
New Class ◽  
Second Derivatives ◽  
Stiff Odes ◽  
Runge Kutta ◽  
Special Case

In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered. The TDTSRK methods are a special case of multi-derivative Runge-Kutta methods proposed by Kastlunger and Wanner (1972). The methods considered herein incorporate only the first and second derivatives terms of ODEs. These methods possess large interval of stability when compared with other existing methods in the literature. The experiments have been performed on standard problems, and comparisons were made with some standard explicit Runge-Kutta methods in the literature.

scholarly journals ORDER OF THE RUNGE-KUTTA METHOD AND EVOLUTION OF THE STABILITY REGION

2019 ◽  
Vol 5 (2) ◽  
pp. 64
Author(s):  
Hippolyte Séka ◽  
Kouassi Richard Assui
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Absolute Stability ◽  
Stability Region ◽  
Kutta Method ◽  
Stability Regions ◽  
Runge Kutta Method ◽  
The Absolute ◽  
Runge Kutta ◽  
The Stability

In this article, we demonstrate through specific examples that the evolution of the size of the absolute stability regions of Runge–Kutta methods for ordinary differential equation does not depend on the order of methods.

THE DYNAMICS OF RUNGE–KUTTA METHODS

1992 ◽  
Vol 02 (03) ◽  
pp. 427-449 ◽  
Author(s):  
JULYAN H. E. CARTWRIGHT ◽  
ORESTE PIRO
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Analysis ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Continuous Time ◽  
Time System ◽  
Integration Schemes ◽  
Runge Kutta ◽  
Continuous Time System

The first step in investigating the dynamics of a continuous-time system described by an ordinary differential equation is to integrate to obtain trajectories. In this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, Runge–Kutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis.

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