scholarly journals On solutions of matrix initial value problems by using differential transform method and convolution

2013 ◽  
Author(s):  
Omer Altun ◽  
Adem Kılıçman
Keyword(s):  
Initial Value Problems ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform

New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Feras Yousef ◽  
Marwan Alquran ◽  
Imad Jaradat ◽  
Shaher Momani ◽  
Dumitru Baleanu
Keyword(s):  
Analytical Study ◽  
Three Dimensional ◽  
Fractional Power ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Models ◽  
Fractional Differential ◽  
Fractional Power Series

Abstract Herein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a γ¯-fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.

scholarly journals POLYNOMIAL SERIES SOLUTION OF BENJAMIN−BONA−MAHONY EQUATION VIA DIFFERENTIAL TRANSFORM METHOD

2020 ◽  
Vol 4 (1) ◽  
pp. 01-03
Author(s):  
Muhammad Jamil ◽  
Badshah- E-Room
Keyword(s):  
General Solution ◽  
Initial Value Problem ◽  
Series Solution ◽  
Initial Conditions ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform ◽  
Polynomial Series

In this work, we solved the initial value problem of Benjamin−Bona−Mahony equation with generalized initial conditions by using differential transform method (DTM). We obtained the general solution in the form of a series. An example is presented for the particular initial conditions.

scholarly journals Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sobhan Mosayebidorcheh
Keyword(s):  
Boundary Layer ◽  
Good Accuracy ◽  
Boundary Layer Equation ◽  
Differential Transform Method ◽  
Algebraic Equations ◽  
Numerical Techniques ◽  
Initial Value ◽  
Pseudoplastic Fluid ◽  
Transform Method ◽  
Differential Transform

The boundary layer equation of the pseudoplastic fluid over a flat plate is considered. This equation is a boundary value problem (BVP) with the high nonlinearity and a boundary condition at infinity. To solve such problems, powerful numerical techniques are usually used. Here, through using differential transform method (DTM), the BVP is replaced by two initial value problems (IVP) and then multi-step differential transform method (MDTM) is applied to solve them. The differential equation and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated in every sub domain. In this solution, there is no need for restrictive assumptions or linearization. Finally, DTM results are compared with the numerical solution of the problem, and a good accuracy of the proposed method is observed.

scholarly journals Enhanced Multistage Differential Transform Method: Application to the Population Models

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Younghae Do ◽  
Bongsoo Jang
Keyword(s):  
Taylor Series ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Initial Condition ◽  
Initial Value ◽  
Transform Method ◽  
Large Domain ◽  
Runge Kutta Method ◽  
Differential Transform

We present an efficient computational algorithm, namely, the enhanced multistage differential transform method (E-MsDTM) for solving prey-predator systems. Since the differential transform method (DTM) is based on the Taylor series, it is difficult to obtain accurate approximate solutions in large domain. To overcome this difficulty, the multistage differential transform method (MsDTM) has been introduced and succeeded to have reliable approximate solutions for many problems. In MsDTM, it is the key to update an initial condition in each subdomain. The standard MsDTM utilizes the approximate solution directly to assign the new initial value. Because of local convergence of the Taylor series, the error is accumulated in a large domain. In E-MsDTM, we propose the new technique to update an initial condition by using integral operator. To demonstrate efficiency of the proposed method, several numerical tests are performed and compared with ones obtained by other numerical methods such as MsDTM, multistage variational iteration method (MVIM), and fourth-order Runge-Kutta method (RK4).

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