A novel computing three-dimensional differential transform method for solving fuzzy partial differential equations

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

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The differential transform method for solving multidimensional partial differential equations

Indian Journal of Science and Technology ◽

10.17485/ijst/2012/v5i2.10 ◽

2012 ◽

Vol 5 (2) ◽

pp. 1-4

Author(s):

H. Jafari

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Differential Transform Method ◽

Partial Differential ◽

Transform Method ◽

Differential Transform

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Analytical Approach to Time-Fractional Partial Differential Equations in Fluid Mechanics

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.347-353.463 ◽

2011 ◽

Vol 347-353 ◽

pp. 463-466

Author(s):

Xue Hui Chen ◽

Liang Wei ◽

Lian Cun Zheng ◽

Xin Xin Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Fluid Mechanics ◽

Approximate Solutions ◽

Differential Transform Method ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Transform Method ◽

Differential Transform ◽

Generalized Differential

The generalized differential transform method is implemented for solving time-fractional partial differential equations in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor’s formula. Results obtained by using the scheme presented here agree well with the numerical results presented elsewhere. The results reveal the method is feasible and convenient for handling approximate solutions of time-fractional partial differential equations.

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Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method

Abstract and Applied Analysis ◽

10.1155/2012/150527 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 2

Author(s):

Younghae Do ◽

Bongsoo Jang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Taylor Series ◽

Nonlinear Partial Differential Equations ◽

Differential Transform Method ◽

Schrödinger Equations ◽

Partial Differential ◽

Transform Method ◽

Differential Transform ◽

Klein Gordon

The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overcome difficulties arising in DTM, we present the new modified version of DTM, namely, the projected differential transform method (PDTM), for solving nonlinear partial differential equations. The proposed method is applied to solve the various nonlinear Klein-Gordon and Schrödinger equations. Numerical approximations performed by the PDTM are presented and compared with the results obtained by other numerical methods. The results reveal that PDTM is a simple and effective numerical algorithm.

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Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2020/v35i830311 ◽

2020 ◽

pp. 34-43

Author(s):

Fadwa A. M. Madi ◽

Fawzi Abdelwahid

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Exact Solutions ◽

Variable Coefficients ◽

Differential Transform Method ◽

Partial Differential ◽

Transform Method ◽

Linear Partial Differential Equations ◽

Differential Transform ◽

Non Linear

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

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