scholarly journals Numerical Solution of First Order Ordinary Differential Equation by Using Runge-Kutta Method

2021 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Kedir Aliyi Koroche
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solution ◽  
Kutta Method ◽  
Order Ordinary Differential Equation ◽  
First 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 A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

2020 ◽  
Vol 17 (1) ◽  
pp. 0166
Author(s):  
Hussain Et al.
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Results ◽  
New Method ◽  
Kutta Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

MULTIDERIVATIVE HYBRID IMPLICIT RUNGE-KUTTA METHOD FOR SOLVING STIFF SYSTEM OF A FIRST ORDER DIFFERENTIAL EQUATION

2018 ◽  
Vol 106 (2) ◽  
pp. 543-562
Author(s):  
Olusheye A. Akinfenwa ◽  
Solomon A. Okunuga ◽  
Blessing I. Akinnukawe ◽  
Uthman O. Rufai ◽  
Ridwanulahi I. Abdulganiy
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Kutta Method ◽  
Stiff System ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta
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