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.

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.

scholarly journals NUMERICAL SIMULATION OF DENGUE FEVER (SIR MODEL) USING DIFFERENTIAL TRANSFORM METHOD, MULTI-STEP DIFFERENTIAL TRANSFORM METHOD AND RK4 METHOD

2021 ◽  
Vol 9 (1) ◽  
pp. 262-272
Author(s):  
Gurpreet Singh Tuteja
Keyword(s):  
Dengue Fever ◽  
Transformation Method ◽  
Sir Model ◽  
Analytic Solutions ◽  
Differential Transform Method ◽  
Step Size ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Differential Transform ◽  
Model Equations

This study investigates the application of the differential transformation method(DTM), multi-step differential transform method(MsDTM) with step-size and RK4 method (Mathematica) for finding the numerical solution of the SIR model of dengue fever in epidemiology. This model is a system of non-linear ordinary differential equations that have no analytic solution. Both the methods DTM and MsDTM are applied directly without any linearization, perturbation or discretization in the model equations to obtain semi-analytic solutions. The accuracy of the MSDTM is excellent and comparable to the RK4 method of Mathematica.

ROLE OF REINFECTION IN TRANSMISSION DYNAMICS OF COVID-19: A SEMI-ANALYTICAL APPROACH USING DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Vol 6 (1) ◽  
pp. 745
Author(s):  
Opeyemi Odetunde ◽  
Jibril Lawal ◽  
Ally Yeketi Ayinla
Keyword(s):  
Treatment Strategies ◽  
Differential Transform Method ◽  
Host Community ◽  
Transmission Dynamics ◽  
Transform Method ◽  
Social Distancing ◽  
Linear System Of Equations ◽  
Differential Transform ◽  
Non Linear System

Reinfection of a recovered individual either as a result of relapse or new contact no doubt poses a major threat to the eradication of an infection within the host community. In this work, the role of re-infection in the transmission dynamics of COVID-19 was considered and analysed using the semi-analytical tool Differential Transform Method (DTM). COVID-19 (also known as Coronavirus) has shut down the economy of the world since it became a global pandemic. A mathematical model was constructed with consideration of multiple pathways of infection transmission, the treatment strategies and policies adopted (social distancing, wearing of face mask and so on) to limit the spread of the infection globally. The non-linear system of equations governing the model was solved using DTM and the resulting series solution was compared with the standard numeric Runge-Kutta order 4 (RK4). It was discovered that re-integration of a recovered individual into the susceptible community without observing the prevention guidelines such as social distancing, washing of hands and proper sanitizing could increase the spread of the infection since the recovered individuals are not guaranteed of immunity against the infection after recovery. The study concluded that families of recovered patients must ensure adequate preventive measure while integrating their recovered loved ones back to their midst.

A robust technique based solution of time-fractional seventh-order Sawada–Kotera and Lax’s KdV equations

2021 ◽  
pp. 2150265
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty ◽  
Dumitru Baleanu ◽  
Waleed Adel ◽  
Hadi Rezazadeh
Keyword(s):  
Convergence Analysis ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
Absolute Error ◽  
Transform Method ◽  
Cpu Time ◽  
Kdv Equations ◽  
Differential Transform ◽  
Seventh Order

In this paper, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada–Kotera (SSK) and Lax’s KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, [Formula: see text] revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values [Formula: see text] are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated.

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.

scholarly journals Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

2020 ◽  
Author(s):  
A. John Christopher ◽  
N. Magesh ◽  
G. Tamil Preethi
Keyword(s):  
Mathematical Model ◽  
Preventive Measures ◽  
Control Strategies ◽  
Transformation Method ◽  
Dynamical Analysis ◽  
Transform Method ◽  
Potential Control ◽  
Corona Virus ◽  
Differential Transform ◽  
The Mathematical Model

Abstract The aim of this paper is applying the Differential Transformation Method (DTM) to analyze and find the solution for the mathematical model described by the system of nonlinear ordinary differential equations which describe the epidemiology of the most threatening virus called Corona-virus later labelled as COVID-19. The behaviour of the outcomes is presented in terms of plots. Finally, the present study may help you to examine the wild class of real world models and also aid to predict their behaviour with respect to parameters considered in the model. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

scholarly journals Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

2015 ◽  
Vol 2 (4) ◽  
pp. 140511 ◽  
Author(s):  
Brajesh K. Singh ◽  
Vineet K. Srivastava
Keyword(s):  
Diffusion Equation ◽  
Fractional Order ◽  
Series Solution ◽  
Approximate Solutions ◽  
Test Problems ◽  
Mathematical Tool ◽  
Transform Method ◽  
Wide Range ◽  
Differential Transform ◽  
Powerful Mathematical Tool

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

scholarly journals Mathematical analysis for Brownian motion of nonlinear thermal bioconvective stagnation point flow in a nanofluid using DTM and RKF method

2020 ◽  
Vol 7 (3) ◽  
pp. 294-307
Author(s):  
Surya Kanta Mondal ◽  
Dulal Pal
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Differential Equations ◽  
Transformation Method ◽  
Stagnation Point Flow ◽  
Transform Method ◽  
Differential Transform ◽  
Nonlinearly Stretching Sheet

Abstract In the present paper, bioconvective stagnation point flow of nanofluid containing gyrotactic microorganisms over a nonlinearly stretching sheet embedded in a porous medium is considered. The scaling group transformation method is introduced to obtain the similarity transformation to convert the governing partial differential equations to a set of ordinary differential equations. The reduced governing nonlinear differential equations are then solved numerically with Runge–Kutta–Fehlberg method. Differential transform method is employed to justify the results obtained by the numerical method. It is found that both the results matched nicely. It is noticed that the density of motile microorganism distribution grows high with an increase in the values of the bioconvection Peclet number. Further, the rate of heat transfer and the rate of mass transfer increase rapidly with an increment in the thermophoresis parameter, heat source parameter, chemical reaction parameter, and Brownian motion parameter, respectively. This work is relevant to engineering and biotechnological applications, such as in the design of bioconjugates and mass transfer enhancement of microfluidics.

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