scholarly journals BEBERAPA KOMBINASI RUNGE-KUTTA UNTUK MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL WAKTU TUNDA

2019 ◽  
Vol 13 (1) ◽  
pp. 13
Author(s):  
Rahma Qudsi ◽  
Agus Dahlia
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Analytic Solutions ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Delay Differential

Delay Differential Equation (DDE) have been applied to  many area. While, we rarely get the analytic solutions of DDE. Many researchers have found many methods to find it for instance Runge-Kutta Method. The purpose of this paper is to accumulate the combinations of Runge-Kutta method which is used to find the solutions of DDE. Keywords : Delay Differential Equation,  Interpolation, Runge-Kutta Method

scholarly journals Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

2019 ◽  
Vol 4 (2) ◽  
pp. 375-386 ◽  
Author(s):  
Vijeyata Chauhan ◽  
Pankaj Kumar Srivastava
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Computational Techniques ◽  
Kutta Method ◽  
Step Method ◽  
Runge Kutta Method ◽  
One Step ◽  
Order And Type ◽  
Runge Kutta ◽  
Delay Differential

The Runge-Kutta method is a one step method with multiple stages, the number of stages determine order of method. The method can be applied to work out on differential equation of the type’s explicit, implicit, partial and delay differential equation etc. The present paper describes a review on recent computational techniques for solving differential equations using Runge-Kutta algorithm of various order. This survey includes the summary of the articles of last decade till recent years based on third; fourth; fifth and sixth order Runge-Kutta methods. Along with this a combination of these methods and various other type of Runge-Kutta algorithm based articles are included. Comparisons of methods with own critical comments as remarks have been included.

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 Nonlinear Parametric Resonance Behavior of Cables in a Long Cantilever Bridge for Sightseeing Platform

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Zengwei Guo ◽  
Pengfei Zi ◽  
Xuanbo He
Keyword(s):  
Differential Equation ◽  
Nonlinear Vibration ◽  
Damping Ratio ◽  
Element Model ◽  
Excitation Amplitude ◽  
Parametric Vibration ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Vibration Performance

In order to study the parametric vibration of stayed cables in a long cantilever bridge for a sightseeing platform, nonlinear parametric vibration equations of the stayed cables excited by the vibration of bridge deck and tower are derived. Then, a second-order differential equation is transformed into a first-order ordinary differential equation, which is solved by using the Runge–Kutta method. A finite element model of cables was also built to verify the solution of the Runge–Kutta method. Then, the inherent dynamic characteristics of the full structure and all the cables with different lengths were analyzed to discuss the potential risk of parametric vibration. The longest and shortest cables were taken as examples to explore their nonlinear vibration performance. The effects of damping ratio, excitation position, and amplitude on cables’ nonlinear vibration performance were investigated. The results show that it will be more efficient and convenient to use the Runge–Kutta method to calculate cables’ nonlinear vibration amplitude without loss of accuracy. In addition, short cables have more resonance zones compared to long cables. Especially, with the cable length shortening, the dominant frequencies of the dynamic response and its amplitude increase significantly, and the number of resonance zones also increases. However, excessive excitation amplitude will also cause multiple resonance zones in the cable. The parametric analysis results show that it is effective and efficient to mitigate the nonlinear vibration by adjusting the frequency relationship between the bridge and the cables, rather than by increasing the damping ratio.

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