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.

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 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.

scholarly journals A Cumulative Study on Differential Transform Method

2019 ◽  
Vol 4 (1) ◽  
pp. 170-181 ◽  
Author(s):  
Geeta Arora ◽  
Pratiksha
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Differential Equations ◽  
Exact Solutions ◽  
Real World ◽  
Analytical Methods ◽  
Analytic Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

Many real-world phenomena when modelled as a differential equation don't generally have exact solutions, so their numerical or analytic solutions are sought after. Differential transform method (DTM) is one of the analytical methods that gives the solution in the form of a power series. In this paper, a cumulative study is done on DTM and its evolution as an effective method to solve the gamut of differential equations.

scholarly journals Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jincun Liu ◽  
Hong Li
Keyword(s):  
Kdv Equation ◽  
Taylor Series Expansion ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Differential Transform Method ◽  
Two Dimensional ◽  
Transform Method ◽  
Coupled Equations ◽  
Differential Transform ◽  
Coupled Kdv Equation

By introducing the fractional derivative in the sense of Caputo and combining the pretreatment technique to deal with long nonlinear items, the generalized two-dimensional differential transform method is proposed for solving the time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equation. The presented method is a numerical method based on the generalized Taylor series expansion which constructs an analytical solution in the form of a polynomial. The numerical results show that the generalized two-dimensional differential transform method is very effective for the fractional coupled equations.

scholarly journals Mixed of Elzaki Transform and Projected Differential Transform Method for a Nonlinear Wave-Like Equations with Variable Coefficients

2018 ◽  
Author(s):  
Ali Khalouta ◽  
Abdelouahab Kadem
Keyword(s):  
Nonlinear Wave ◽  
Transformation Method ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Differential Transformation Method ◽  
Transform Method ◽  
Differential Transformation ◽  
Differential Transform

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

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.

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