scholarly journals Third-Order Improved Runge-Kutta Method for Solving Ordinary Differential Equation

2011 ◽  
pp. 191-194 ◽  
Author(s):  
Faranak rabiei ◽  
Fudziah Ismail
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Kutta Method ◽  
Third Order ◽  
Runge Kutta Method ◽  
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 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.

scholarly journals A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Mechee ◽  
N. Senu ◽  
F. Ismail ◽  
B. Nikouravan ◽  
Z. Siri
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Film Flow ◽  
New Method ◽  
Kutta Method ◽  
Thin Film Flow ◽  
Third Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

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