scholarly journals NUMERICAL SOLUTION FOR IMMUNOLOGY TUBERCULOSIS MODEL USING RUNGE KUTTA FEHLBERG AND ADAMS BASHFORTH MOULTON METHOD

2016 ◽  
Vol 78 (5) ◽  
Author(s):  
Usman Pagalay ◽  
Muhlish Muhlish
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Relative Error ◽  
Nonlinear Differential Equations ◽  
High Accuracy ◽  
First Order ◽  
Tuberculosis Model ◽  
Runge Kutta

The Immunology tuberculosis model that has been formulated by (Ibarguen, E., Esteva, L., & Chavez, L, 2011) in the form of a system of nonlinear differential equations first order. In this study, we used to Runge Kutta Fehlberg method and Adams Bashforth Moulton method. This study has been obtained numerical solution of the model. The results showed that the relative error obtained from the Adams Bashforth Moulton method is smaller when compared with the Runge Kutta Fehlber method. There are two methods has a high accuracy in solving systems of nonlinear differential equations.

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.

scholarly journals Novel Exponentially Fitted Two-Derivative Runge-Kutta Methods with Equation-Dependent Coefficients for First-Order Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yanping Yang ◽  
Yonglei Fang ◽  
Xiong You ◽  
Bin Wang
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Results ◽  
First Order ◽  
Truncation Errors ◽  
New Methods ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
First Order Differential Equations

The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK) methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

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