https://qspace.qu.edu.qa/bitstream/handle/10576/10623/A%20generalized%20differential%20transform%20method%20for%20linear%20partial%20differential%20equations%20of%20fractional%20order%20.pdf;sequence=1

A generalized differential transform method for linear partial differential equations of fractional order

Generalized differential transform method : Application to differential equations of fractional order

Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation

The differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. This new algorithm is applied to Lotka-Volterra, Chen and Lorenz systems. Then, a comparative study between the new algorithm, multi-step DTM, classical DTM and the classical Runge-Kutta method is presented. The results demonstrate reliability and efficiency of the algorithm developed.

https://hal.archives-ouvertes.fr/hal-00430504/document

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Papers

Solution of different type of the partial differential equation by differential transform method and Adomian’s decomposition method