Details

The -order Taylor series expansion function of is of the form . At , this is the Maclaurin series, . The differential transformation of the function is given by . The differential inverse transform of is defined by . Table 1 in [2] gives a list of properties of the differential transformation. For instance, if then .

References

[1] M. J. Jang, C. L. Chen, and Y. C. Liu, "Analysis of the Response of a Strongly Nonlinear Damped System Using a Differential Transformation Technique," Applied Mathematics and Computation, 88(2–3) 1997 pp. 137–151. doi: 10.1016/S0096-3003(96)00308-6.

[2] C. L. Chen and Y. C. Liu, "Solution of Two-Boundary-Value Problems Using the Differential Transformation Method," Journal of Optimization Theory and Applications, 99(1), 1998 pp. 23–35. doi: 10.1023/A:1021791909142.

[3] M. J. Jang, C. L. Chen, and Y. C. Liu, "On Solving the Initial-Value Problems Using the Differential Transformation Method," Applied Mathematics and Computation, 115(2–3), 2000 pp. 145–160. doi: 10.1016/S0096-3003(99)00137-X.

[4] A. A. Joneidi, D. D. Ganji, and M. Babaelahi, "Differential Transformation Method to Determine Fin Efficiency of Convective Straight Fins with Temperature Dependent Thermal Conductivity," International Communications in Heat and Mass Transfer, 36(7), 2009 pp. 757–62. doi: 10.1016/j.icheatmasstransfer.2009.03.020.