### Efficient Developments to Heuristic Approach of the General Form of the Differential Transformation Algorithms

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#### Abstract

In this paper, efficient developments are pursued on the Differential Transformation Method algorithms. These developments are able to reduce the amount of time used to carry out these algorithms by locating and truncating number of the unnecessary calculated terms. Implementing the modified algorithms demonstrates rapid performance in obtaining results. Hence, the proposed developments are reliable and efficient in decreasing the time cost elapsed in computing the terms of the series solution without encountering any impact in accuracy performance. *Copyright © 2015 Praise Worthy Prize - All rights reserved.*

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F. Mirzaee, Differential Transform Method for Solving Linear and Nonlinear Systems of Ordinary Differential Equations, Applied Mathematical Sciences, vol. 5 n. 70, 2001, pp. 3465 -- 3472.

M. Jang, C. Chen, Y. Liu, Two-dimensional differential transform for partial differential equations, Applied Mathematics and Computation, vol. 121 n. 2-3, 2001, pp. 261-270.

http://dx.doi.org/10.1016/s0096-3003(99)00293-3

M. Odibat, Differential transform method for solving Volterra integral equation with separable kernels, Mathematical and Computer Modelling, vol. 48 n. 7-8, 2008, pp. 1144--1149.

http://dx.doi.org/10.1016/j.mcm.2007.12.022

K. R. Raslan, A. Biswas, F. Abu Sheer, Differential transform method for solving partial differential equations with variable coefficients, International Journal of Physical Sciences, vol. 7 n. 9, 2012, pp. 1412 -- 1419.

http://dx.doi.org/10.5897/ijps11.1770

R. Kanth, K. Aruna, Differential Transform Method for Solving the Linear and Nonlinear Klein--Gordon Equation, Computer Physics Communications Journal, vol. 180 n. 5, 2009, pp. 708-711.

http://dx.doi.org/10.1016/j.cpc.2008.11.012

H. Fatoorehchi, H. Abolghasemi, Differential Transform Method to Investigate Mass Transfer Phenomenon to a Falling Liquid Film System, Australian Journal of Basic and Applied Sciences, vol. 5 n. 3, 2011, pp. 337-345.

J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits (Huazhong University Press, Inc., 1986).

C. K. Chen, S.H. Ho, Application of Differential Transformation to Eigenvalue Problems, Journal of Applied Mathematics and Computation, vol. 79 n. 2-3, 1996, pp. 173-188.

http://dx.doi.org/10.1016/0096-3003(95)00253-7

Z. Odibat, S. Momani, A generalized differential transform method for linear partial differential equations of fractional order, Applied Mathematics Letters, vol. 21 n. 2, 2007, pp. 194-199.

http://dx.doi.org/10.1016/j.aml.2007.02.022

A. Tari, S. Shahmorad, Differential transform method for the system of two-dimensional nonlinear Volterra integro-differential equations, Computers and Mathematics with Applications, vol. 61 n. 9, 2011, pp. 2621--2629.

http://dx.doi.org/10.1016/j.camwa.2011.03.007

Y. Keskin, (2010). Ph.D. Thesis, University of Selcuk.

N. J. Higham, Accuracy and stability of numerical algorithms (Society for Industrial and Applied Mathematics, Inc., 1996).

N. Kalinnik, M. Korch, T. Rauber, An efficient time-step-based self-adaptive algorithm for predictor--corrector methods of Runge--Kutta type, Journal of Computational and Applied Mathematics, vol. 236 n. 3, 2011, pp. 394-410.

http://dx.doi.org/10.1016/j.cam.2011.07.015

A. Greenbaum, T. P. Chartier, Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms (Princeton University Press, Inc. 2012).

R. Abazari, M. Abazari, Numerical simulation of generalized Hirota--Satsuma coupled KdV equation by RDTM and comparison with DTM, Communications in Nonlinear Sciences and Numerical Simulation, vol. 17 n. 2, 2012, pp. 619--629.

http://dx.doi.org/10.1016/j.cnsns.2011.05.022

H. Taghvafard and G. H. Erjaee, Two-dimensional Differential Transform Method for Solving Linear and Non-linear Goursat Problem, International Journal of Information and Mathematical Sciences, vol. 6 n. 2, 2010.

AbuGhannam, N., Suwan, I., Hybrid Numerical-Analytical Approach for Linear and Nonlinear Elliptic Partial Differential Equations Based on the Two-Dimensional Differential Transformation Method, (2013) International Journal on Numerical and Analytical Methods in Engineering (IRENA), 1 (5), pp. 237-244.

Keskin, Y., G. Oturanc, Numerical Solution of Regularized Long Wave Equation by Reduced Differential Transform Method, Applied Mathematical Sciences, vol. 4 n. 25, 2010, pp. 1221 -- 1231.

AbuGhannam, N., Suwan, I., Semi-Numerical Analytical Solution to Linear and Nonlinear Heat Equations via the Reduced Differential Transformation Method, (2013) International Journal on Heat and Mass Transfer - Theory and Applications (IREHEAT), 1 (4), pp. 235-241.

D. Logan, An Introduction To NonLinear Partial Differential Equation (Fifth Edition, Hoboken , N.J. John Wiley & Sons. Inc., 2008).

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