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Adomian decomposition method for nonlinear differential-difference equations. (English) Zbl 1221.65209
Summary: We extend the Adomian decomposition method (ADM) to find the approximate solutions for the nonlinear differential-difference equations (NDDEs), such as the discretized mKdV lattice equation, the discretized nonlinear Schrödinger equation and the Toda lattice equation. By comparing the approximate solutions with the exact analytical solutions, we find the extend method for NDDEs is of good accuracy.
MSC:
65L99Numerical methods for ODE
References:
[1]Fermi, E.; Pasta, J.; Ulam, S.: Collected papers of enrico Fermi II, (1965)
[2]Scott, A. C.; Macheil, L.: Binding energy versus nonlinearity for a small stationary soliton, Phys lett A 98, 87-88 (1983)
[3]Sievers, A. J.; Takeno, S.: Intrinsic localized modes in anharmonic crystals, Phys rev lett 61, 970-973 (1988)
[4]Su, W. P.; Schrieffer, J. R.; Heege, A. J.: Solitons in polyacetylene, Phys rev lett 42, 1698-1701 (1979)
[5]Davydov, A. S.: The theory of contraction of proteins under their excitation, J theor biol 38, 559-569 (1973)
[6]Marquii, P.; Bilbault, J. M.; Rernoissnet, M.: Observation of nonlinear localized modes in an electrical lattice, Phys rev E 51, 6127-6133 (1995)
[7]Eisenberg, H. S.; Silberberg, Y.; Morandotti, R.; Boyd, A. R.; Aitchison, J. S.: Discrete spatial optical solitons in waveguide arrays, Phys rev lett 81, 3383-3386 (1998)
[8]Morandotti, R.; Peschel, U.; Aitchison, J. S.; Eisenberg, H. S.; Silberberg, Y.: Dynamics of discrete solitons in optical waveguide arrays, Phys rev lett 83, 2726-2729 (1999)
[9]Suris, Yu.B.: New integrable systems related to the relativistic Toda lattice, J phys A: math gen 30, 1745-1761 (1997) · Zbl 1001.37508 · doi:10.1088/0305-4470/30/5/035
[10]Suris, Yu.B.: On some integrable systems related to the Toda lattice, J phys A: math gen 30, 2235-2249 (1997) · Zbl 0935.37037 · doi:10.1088/0305-4470/30/6/041
[11]Suris, Yu.B.: A discrete-time relativistic Toda lattice, J phys A: math gen 29, 451-465 (1996) · Zbl 0916.58014 · doi:10.1088/0305-4470/29/2/022
[12]Suris YuB. Miura transformations for Toda-type integrable systems, with applications to the problem of integrable discretizations, Sfb288 Preprint 367. Department of Mathematics, Technical University Berlin, Berlin, Germany, 2001.
[13]Suris YuB. The problem of integrable discretization: Hamiltonian approach. A skeleton of the book, Sfb288 Preprint 479. Department of Mathematics, Technical University Berlin, Berlin, Germany, 2002.
[14]Adomian, G.: Stochastic system, (1983)
[15]Adomian, G.: Solving frontier problem of physics: the decomposition method, (1994)
[16]Adomian, G.: Solution of the Thomas – Fermi equation, Appl math lett 11, 131-133 (1998) · Zbl 0947.34501 · doi:10.1016/S0893-9659(98)00046-9
[17]Wazwaz, Abdul-Majid: A computational approach to soliton solutions of the Kadomtsev – Petviashvili equation, Appl math comput 123, 205-217 (2001) · Zbl 1024.65098 · doi:10.1016/S0096-3003(00)00065-5
[18]Wazwaz, Abdul-Majid: The decomposition method applied to systems of partial differential equations and to the reaction – diffusion Brusselator model, Appl math comput 110, 251-264 (2000) · Zbl 1023.65109 · doi:10.1016/S0096-3003(99)00131-9
[19]Kaya, D.; El-Sayed, S. M.: Numerical soliton-like solutions of the potential Kadomtsev – Petviashvili equation by the decomposition method, Phys lett A 320, 192-199 (2003) · Zbl 1065.35219 · doi:10.1016/j.physleta.2003.11.021
[20]El-Danaf, Talaat S.; Ramadan, Mohamed A.; Alaal, Faysal E. I. Abd: The use of Adomian decomposition method for solving the regularized long-wave equation, Chaos soliton fract 26, 747-757 (2005) · Zbl 1073.35010 · doi:10.1016/j.chaos.2005.02.012
[21]Abdou, M. A.: J quant spectrosc radiat transfer, J quant spectrosc radiat transfer 95, 407 (2005)
[22]Ablowitz, M. J.; Ladic, J. F.: On the solution of a class of nonlinear partial difference equations, Stud appl math 57, 1-12 (1977) · Zbl 0384.35018
[23]Dai, C. Q.; Zhang, J. F.: Jacobian elliptic function method for nonlinear differential-difference equations, Chaos soliton fract 27, 1042-1047 (2006) · Zbl 1091.34538 · doi:10.1016/j.chaos.2005.04.071