Solution of differential-difference equations by using differential transform method. (English) Zbl 1148.65310

Summary: We successfully extended the differential transform method, by presenting and proving new theorems, to the solution of differential-difference equations (DDEs). Theorems are presented in the most general form to cover a wide range of DDEs, being linear or nonlinear and the constant or variable coefficients. In order to show the power and the robustness of the method and to illustrate the pertinent features of related theorems, examples are presented.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34K10 Boundary value problems for functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
Full Text: DOI


[1] Fermi, E.; Pasta, J.; Ulam, S., Collected papers of enrico Fermi II, (1965), University of Chicago Press Chicago, IL
[2] Ablowitz, M.J.; Ladik, J.F., A nonlinear difference scheme and inverse scattering, Stud. appl. math., 55, 213-229, (1976) · Zbl 0338.35002
[3] Hu, X.B.; Ma, W.X., Application of hirota’s bilinear formalism to the Toeplitz lattice—some special soliton-like solutions, Phys. lett. A, 293, 161-165, (2002) · Zbl 0985.35072
[4] Fan, E., Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled mkdv equation, Phys. lett. A, 282, 18-22, (2001) · Zbl 0984.37092
[5] Dai, C.; Zhang, J., Jacobian elliptic function method for nonlinear differential-difference equations, Chaos, soliton fract., 27, 1042-1047, (2006) · Zbl 1091.34538
[6] Elmer, C.E.; van Vleck, E.S., Travelling wave solutions for bistable differential-difference equations with periodic diffusion, SIAM J. appl. math., 61, 1648-1679, (2001) · Zbl 0981.35020
[7] Elmer, C.E.; van Vleck, E.S., A variant of newton’s method for solution of traveling wave solutions of bistable differential-difference equation, J. dyn. differen. equat., 14, 493-517, (2002) · Zbl 1007.65062
[8] Sezer, M.; Akyuz-Dascioglu, A., Taylor polynomial solutions of general linear differential-difference equations with variable coefficients, Appl. math. comput., 174, 753-765, (2006)
[9] Gulsu, M.; Sezer, M., A Taylor polynomial approach for solving differential-difference equations, J. comput. appl. math., 186, 2, 349-364, (2006) · Zbl 1078.65551
[10] Zhou, J.K., Differential transformation and its application for electrical circuit, (1986), Huazhong University Press Wuhan, China
[11] Arikoglu, A.; Ozkol, I., Analysis for slip flow over a single free disk with heat transfer, J. fluid. eng.—T ASME, 127, 624-627, (2005)
[12] A. Arikoglu, I. Ozkol, On the MHD and slip flow over a rotating disk with heat transfer, Int. J. Numer. Method H, in press. · Zbl 1231.76342
[13] Arikoglu, A.; Ozkol, I., Inner-outer matching solution of Blasius equation by DTM, Aircr. eng. aerosp. tech., 77, 298-301, (2005)
[14] Arikoglu, A.; Ozkol, I., Solution of boundary value problems for integro-differential equations by using differential transform method, Appl. math. comput., 168, 1145-1158, (2005) · Zbl 1090.65145
[15] Arikoglu, A.; Ozkol, I., Solution of difference equations by using differential transform method, Appl. math. comput., 174, 442-454, (2006)
[16] Levy, H.; Lesman, F., Finite difference equations, (1961), The Macmillian Company New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.