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 Approximate Analytic Solutions of Two-Dimensional Nonlinear Klein–Gordon Equation by Using the Reduced Differential Transform Method

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wayinhareg Gashaw Belayeh ◽  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Type Systems ◽  
Analytical Approximation ◽  
Differential Transform Method ◽  
Two Dimensional ◽  
Transform Method ◽  
Differential Transform ◽  
Klein Gordon ◽  
Reduced Differential Transform Method

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear Klein–Gordon equations (NLKGEs) with quadratic and cubic nonlinearities subject to appropriate initial conditions. The proposed technique has the advantage of producing an analytical approximation in a convergent power series form with a reduced number of calculable terms. Two test examples from mathematical physics are discussed to illustrate the validity and efficiency of the method. In addition, numerical solutions of the test examples are presented graphically to show the reliability and accuracy of the method. Also, the results indicate that the introduced method is promising for solving other type systems of NLPDEs.

Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation

2010 ◽  
Vol 19 (8) ◽  
pp. 080204 ◽  
Author(s):  
Zhao Guo-Zhong ◽  
Yu Xi-Jun ◽  
Xu Yun ◽  
Zhu Jiang ◽  
Wu Di
Keyword(s):  
Kdv Equation ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Coupled Kdv Equation

Application of Differential Transform Method to Buckling Problems at Clamped-Free Boundary Conditions

2013 ◽  
Vol 639-640 ◽  
pp. 818-822
Author(s):  
Ling Feng Han ◽  
Shi Yuan Wu
Keyword(s):  
Free Boundary ◽  
Taylor Series ◽  
Critical Length ◽  
Taylor Series Expansion ◽  
Differential Transform Method ◽  
Transform Method ◽  
Free Boundary Conditions ◽  
Differential Transform ◽  
Taylor Series Method ◽  
Engineering Mechanics

Differential Transform Method (DTM) is a new semi-analytical, semi-numerical algorithm, which transforms differential equations to the form of Taylor series. The method derives an approximate numerical solution based on Taylor series expansion, which is a analytical solution built on polynomial form. Traditional Taylor series method is used for symbolic computation, while the Differential Transform Method obtained the solution of the polynomials through itineration calculations. Applying DTM to buckling problems, the critical length of a bar at clamped-free boundary is studied. The computational results are compared with analytical solutions and shown excellent agreement between those two algorithms. The method adds a new tool for computational engineering mechanics.

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.

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.

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