Differential Transform Method for Some Delay Differential Equations


This paper concentrates on the differential transform method (DTM) to solve some delay differential equations (DDEs). Based on the method of steps for DDEs and using the computer algebra system Mathematica, we successfully apply DTM to find the analytic solution to some DDEs, including a neural delay differential equation. The results confirm the feasibility and efficiency of DTM.

Share and Cite:

Liu, B. , Zhou, X. and Du, Q. (2015) Differential Transform Method for Some Delay Differential Equations. Applied Mathematics, 6, 585-593. doi: 10.4236/am.2015.63053.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Pukhov, G.E. (1986) Differential Transformations and Mathematical Modelling of Physical Processes. Naukova Dumka, Kiev.
[2] Zhou, J.K. (1986) Differential Transformation and Its Application for Electrical Circuits. Huazhong University Press, Wuhan. (In Chinese)
[3] Ayaz, F. (2004) Solutions of the System of Differential Equations by Differential Transform Method. Applied Mathematics and Computation, 147, 547-567.
[4] Kurnaz, A., Oturnaz, G. and Kiris, M.E. (2005) n-Dimensional Differential Transformation Method for Solving PDEs. International Journal of Computer Mathematics, 82, 369-380.
[5] Ayaz, F. (2004) Applications of Differential Transform Method to Differential-Algebraic Equations. Applied Mathematics and Computation, 152, 649-657.
[6] Liu, H. and Song, Y.Z. (2007) Differential Transform Method Applied to High Index Differential-Algebraic Equations. Applied Mathematics and Computation, 184, 748-753.
[7] Abdel-Halim Hassan, I.H. (2002) On Solving Same Eigenvalue Problems by Using a Differential Transformation. Applied Mathematics and Computation, 127, 1-22.
[8] Biazar, J., Eslami, M. and Islam, M.R. (2012) Differential Transform Method for Special Systems of Integral Equations. Journal of King Saud University (Science), 24, 211-214.
[9] Shadia, M. (1992) Numerical Solution of Delay Differential and Neutral Differential Equations Using Spline Methods. Ph.D. Thesis, Assuit University, Assuit.
[10] El-Hawary, H.M. and Mahmoud, S.M. (2003) Spline Collocation Methods for Solving Delay-Differential Equations. Applied Mathematics and Computation, 146, 359-372.
[11] Evans, D.J. and Raslan, K.R. (2005) The Adomian Decomposition Method for Solving Delay Differential Equation. International Journal of Computer Mathematics, 82, 49-54.
[12] Vanani, S.K. and Aminataei, A. (2008) On the Numerical Solution of Neutral Delay Differential Equations Using Multiquadric Approximation Scheme. Bulletin of the Korean Mathematical Society, 45, 663-670.
[13] Karako, F. and Bereketoglu, H. (2009) Solutions of Delay Differential Equations by Using Differential Transform Method. International Journal of Computer Mathematics, 86, 914-923.
[14] Lainscsek, C. and Sejnowski, T.J. (2015) Delay Differential Analysis of Time Series. Neural Computation, 27, 594-614.
[15] Abazari, R. and Kilicman, A. (2014) Application of Differential Transform Method on Nonlinear Integro-Differential Equations with Proportional Delay. Neural Computing and Applications, 24, 391-397.
[16] Driver, R.D. (1977) Ordinary and Delay Differential Equations. Applied Mathematical Sciences, 20.
[17] Odibat, Z.M., et al. (2010) A Multi-Step Differential Transform Method and Application to Non-Chaotic or Chaotic Systems. Computers & Mathematics with Applications, 59, 1462-1472.
[18] Hairer, E., et al. (1993) Solving Ordinary Differential Equations I: Nonstiff Problems. 2nd Edition, Springer-Verlag, Berlin.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.