Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

SERIES SOLUTION OF TYPHOID FEVER MODEL USING DIFFERENTIAL TRANSFORM METHOD

2018 ◽  
Vol 3 (1) ◽  
pp. 67
Author(s):  
O J Peter ◽  
Oluwaseun B Akinduko ◽  
C Y Ishola ◽  
O A Afolabi ◽  
A B Ganiyu
Keyword(s):  
Typhoid Fever ◽  
Disease Transmission ◽  
Series Solution ◽  
Transformation Method ◽  
Type Model ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Model Equations ◽  
Non Linear System

This paper presents an analysis of PSIuIeTR type model, which are used to study the transmission dynamics of typhoid fever diseases in a population. Basic idea of typhoid fever disease transmission using compartmental modeling is discussed. Differential Transformation Method (DTM) is discussed in detail, which is used to compute the series solution of the non-linear system of differential equation governing the model equations. The validity of the (DTM) in solving the proposed model is established by classical fourth-order Runge-Kutta method which is implemented in Maple 18. Graphical results confirm that (DTM) is in good agreement with RK-4 and this produced correctly same behaviour of the model, thus validating the efficiency and accuracy of (DTM) in finding the series solution of an epidemic model.

scholarly journals Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shaher Momani ◽  
Asad Freihat ◽  
Mohammed AL-Smadi
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense. Furthermore, we present figurative comparisons between the proposed scheme and the classical fourth-order Runge-Kutta method to demonstrate the accuracy and applicability of this method. The graphical results reveal that only few terms are required to deduce the approximate solutions which are found to be accurate and efficient.

Comparison of Numerical Methods of the SEIR Epidemic Model of Fractional Order

2014 ◽  
Vol 69 (1-2) ◽  
pp. 81-89 ◽  
Author(s):  
Anwar Zeb ◽  
Madad Khan ◽  
Gul Zaman ◽  
Shaher Momani ◽  
Vedat Suat Ertürk
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Nonnegative Solution ◽  
Incidence Rates ◽  
Kutta Method ◽  
Transform Method ◽  
Seir Model ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model by taking into account both standard and bilinear incidence rates of fractional order. First, the nonnegative solution of the SEIR model of fractional order is presented. Then, the multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. Finally, the obtained results are compared with those obtained by the fourth-order Runge-Kutta method and non-standard finite difference (NSFD) method in the integer case.

scholarly journals Application of the Multistep Generalized Differential Transform Method to Solve a Time-Fractional Enzyme Kinetics

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Alawneh
Keyword(s):  
Enzyme Kinetics ◽  
Fractional Derivatives ◽  
Differential Transform Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Kutta Method ◽  
Transform Method ◽  
Enzyme Substrate ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

The multistep differential transform method is first employed to solve a time-fractional enzyme kinetics. This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The results demonstrate reliability and efficiency of the algorithm developed.

scholarly journals A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations

2020 ◽  
Vol 25 (2) ◽  
pp. 122-129
Author(s):  
M.M. Rashidi ◽  
F. Rabiei ◽  
S. Naseri Nia ◽  
S. Abbasbandy
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Differential Equations ◽  
Analytical Method ◽  
Transformation Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Different Types ◽  
Integral Differential Equations

AbstractIn this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.

An Application of the Differential Transform Method to the Biochemical Reaction Systems

2013 ◽  
Vol 319 ◽  
pp. 151-156
Author(s):  
Mustafa Bayram ◽  
Kenan Yildirim ◽  
Muhammet Kurulay
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Its Region ◽  
Differential Transform Method ◽  
Biochemical Reaction ◽  
Power Series Solution ◽  
Transform Method ◽  
Reaction Systems ◽  
Differential Transform ◽  
Theoretical Considerations

An approximate analytical solution for the biochemical reaction systems is derived using the differential transform method. The analytical solution, which is given in the form of a power series, is found to be highly accurate in predicting the behavior of the reaction in the very early stages. To accelerate the convergence of the power series solution and extend its region of applicability throughout the entire transient phase, we used differential transform method theoretical considerations has been discussed and some examples were presented to show the ability of the method for Biochemical reaction systems. We use MAPLE computer algebra system to solve given problems[4].

An Approximate Analytical Solution of Richards’ Equation

2015 ◽  
Vol 16 (5) ◽  
pp. 239-247 ◽  
Author(s):  
Xi Chen ◽  
Ying Dai
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
Traveling Wave ◽  
Wave Solution ◽  
Approximate Analytical Solution ◽  
Traveling Wave Solution ◽  
Richards Equation ◽  
Transform Method ◽  
Differential Transform ◽  
Finite Layer

AbstractAn approximate analytical solution of Richards’ equation (RE) in a semi-finite layer of porous medium is obtained in this article. The basic idea is constructing a function between the Boltzmann variable ϕ and the traveling wave solution of RE, introducing the function into RE and calculating the relevant parameters by differential transform method (DTM). In the end, three examples are prepared to show the accuracy of the presented approximate analytical solution.

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