scholarly journals Comparison of Numerical Simulation of Epidemiological Model between Euler Method with 4th Order Runge Kutta Method

2021 ◽  
Vol 2 (1) ◽  
pp. 37-44
Author(s):  
Rizky Ashgi
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Sir Model ◽  
Euler Method ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Global Pandemic ◽  
The World ◽  
Runge Kutta

Coronavirus Disease 2019 has become global pandemic in the world. Since its appearance, many researchers in world try to understand the disease, including mathematics researchers. In mathematics, many approaches are developed to study the disease. One of them is to understand the spreading of the disease by constructing an epidemiology model. In this approach, a system of differential equations is formed to understand the spread of the disease from a population. This is achieved by using the SIR model to solve the system, two numerical methods are used, namely Euler Method and 4th order Runge-Kutta. In this paper, we study the performance and comparison of both methods in solving the model. The result in this paper that in the running process of solving it turns out that using the euler method is faster than using the 4th order Runge-Kutta method and the differences of solutions between the two methods are large.

scholarly journals Comparative Study on Results of Euler, Improved Euler and Runge-Kutta Methods for Solving the Engineering Unknown Problems

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Khaing Khaing Lwin
Keyword(s):  
Numerical Methods ◽  
Comparative Study ◽  
Fourth Order ◽  
Teaching And Learning ◽  
Euler Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Engineering Problems ◽  
Runge Kutta ◽  
The Difference

The paper presents the comparative study on numerical methods of Euler method, Improved Euler method and fourth-order Runge-Kutta method for solving the engineering problems and applications. The three proposed methods are quite efficient and practically well suited for solving the unknown engineering problems. This paper aims to enhance the teaching and learning quality of teachers and students for various levels. At each point of the interval, the value of y is calculated and compared with its exact value at that point. The next interesting point is the observation of error from those methods. Error in the value of y is the difference between calculated and exact value. A mathematical equation which relates various functions with its derivatives is known as a differential equation. It is a popular field of mathematics because of its application to real-world problems. To calculate the exact values, the approximate values and the errors, the numerical tool such as MATLAB is appropriate for observing the results. This paper mainly concentrates on identifying the method which provides more accurate results. Then the analytical results and calculates their corresponding error were compared in details. The minimum error directly reflected to realize the best method from different numerical methods. According to the analyses from those three approaches, we observed that only the error is nominal for the fourth-order Runge-Kutta method.

scholarly journals Resolução Numérica da equação diferencial de resfriamento de newton pelos métodos de EULER e RUNGE-KUTTA

2016 ◽  
Vol 2 (1) ◽  
pp. 10-25
Author(s):  
Andresa Pescador ◽  
Zilmara Raupp Quadros Oliveira
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Euler Method ◽  
Kutta Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Analytical Resolution ◽  
Important Branch ◽  
First Order Differential Equations

This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.

Accuracy and Reliability of Piecewise-Constant Method in Studying the Responses of Nonlinear Dynamic Systems

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Liming Dai ◽  
Xiaojie Wang ◽  
Changping Chen
Keyword(s):  
Numerical Methods ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamic Systems ◽  
Processing Unit ◽  
Kutta Method ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Accuracy and reliability of the numerical simulations for nonlinear dynamical systems are investigated with fourth-order Runge–Kutta method and a newly developed piecewise-constant (P-T) method. Nonlinear dynamic systems with external excitations are studied and compared with the two numerical approaches. Semianalytical solutions for the dynamic systems are developed by the P-T approach. With employment of a periodicity-ratio (PR) method, the regions of regular and irregular motions are determined and graphically presented corresponding to the system parameters, for the comparison of accuracy and reliability of the numerical methods considered. Central processing unit (CPU) time executed in the numerical calculations with the two numerical methods are quantitatively investigated and compared under the same computational conditions. Due to its inherent drawbacks, as found in the research, Runge–Kutta method may cause information missing and lead to incorrect conclusions in comparing with the P-T method.

scholarly journals A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Sarmad Arshad ◽  
Dumitru Baleanu ◽  
Muhammad Bilal Riaz ◽  
Muhammad Abbas
Keyword(s):  
Growth Model ◽  
Euler Method ◽  
Logistic Growth ◽  
The Novel ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Novel Method ◽  
Fractional Differential ◽  
Logistic Growth Model ◽  
Runge Kutta

In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.

Research on Numerical Simulation of Quad Bundle Conductor on Galloping

2013 ◽  
Vol 457-458 ◽  
pp. 23-27
Author(s):  
Xue Ping Zhan ◽  
Kuan Jun Zhu ◽  
Cao Lan Liu ◽  
Bin Liu ◽  
Jun Zhang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Kutta Method ◽  
Aerodynamic Parameter ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta ◽  
Element Method

The models of the multi-bundled conductors are constructed by finite element method in this paper. The numerical results are given by using the 4th order Runge-Kutta method considering aerodynamic parameter of sub-conductor. The simulation results are obtained on galloping of quad bundle conductors with the different span. Thus some effective numerical results of quad twin bundle conductor can provide a useful reference for anti-galloping design.

Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields

2016 ◽  
Vol 07 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Beibei Zhu ◽  
Zhenxuan Hu ◽  
Yifa Tang ◽  
Ruili Zhang
Keyword(s):  
Numerical Simulation ◽  
Hamiltonian System ◽  
Second Order ◽  
Symplectic Methods ◽  
Kutta Method ◽  
Numerical Accuracy ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta

We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system. The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation. Furthermore, they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.

scholarly journals Optimum Integration Procedure for Connectionist and Dynamic Field Equations

2021 ◽  
Vol 15 ◽  
Author(s):  
Andrés Rieznik ◽  
Rocco Di Tella ◽  
Lara Schvartzman ◽  
Andrés Babino
Keyword(s):  
Euler Method ◽  
Connectionist Model ◽  
Kutta Method ◽  
Field Equations ◽  
Single Digit ◽  
First Order ◽  
Runge Kutta Method ◽  
Dynamic Field ◽  
Runge Kutta ◽  
First Order Differential Equations

Connectionist and dynamic field models consist of a set of coupled first-order differential equations describing the evolution in time of different units. We compare three numerical methods for the integration of these equations: the Euler method, and two methods we have developed and present here: a modified version of the fourth-order Runge Kutta method, and one semi-analytical method. We apply them to solve a well-known nonlinear connectionist model of retrieval in single-digit multiplication, and show that, in many regimes, the semi-analytical and modified Runge Kutta methods outperform the Euler method, in some regimes by more than three orders of magnitude. Given the outstanding difference in execution time of the methods, and that the EM is widely used, we conclude that the researchers in the field can greatly benefit from our analysis and developed methods.

scholarly journals A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Mohammad Asif Arefin
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Euler Method ◽  
Euler’S Method ◽  
Runge Kutta Method ◽  
Accuracy Level ◽  
Runge Kutta ◽  
Matlab Programming

In this paper, the initial value problem of Ordinary Differential Equations has been solved by using different Numerical Methods namely Euler’s method, Modified Euler method, and Runge-Kutta method. Here all of the three proposed methods have to be analyzed to determine the accuracy level of each method. By using MATLAB Programming language first we find out the approximate numerical solution of some ordinary differential equations and then to determine the accuracy level of the proposed methods we compare all these solutions with the exact solution. It is observed that numerical solutions are in good agreement with the exact solutions and numerical solutions become more accurate when taken step sizes are very much small. Lastly, the error of each proposed method is determined and represents them graphically which reveals the superiority among all the three methods. We fund that, among the proposed methods Runge-Kutta 4th order method gives the accurate result and minimum amount of error.

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