Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] aduj_v1_0.tar.gz(24 Kbytes)|
|Manuscript Title: Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations|
|Authors: D. Baldwin, Ü. Göktas, W. Hereman|
|Program title: DDESpecialSolutions.m|
|Catalogue identifier: ADUJ_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 162(2004)203|
|Programming language: Mathematica, version 3.0 or higher.|
|Computer: Created using a PC, but can be run on UNIX and Apple machines.|
|Operating system: Windows 2000 and XP.|
|RAM: 9 MB|
|Keywords: Exact solutions, traveling wave solutions, differential-difference equations, semi-discrete lattices, tanh-method.|
|PACS: 02.70.Wz, 02.30.Ik, 02.30.Jr, 02.90.+p.|
|Classification: 5, 4.3.|
Nature of problem:
The program computes exact solutions to differential-difference equations in terms of the tanh function. Such solutions describe particle vibrations in lattices, currents in electrical networks, pulses in biological chains, etc.
After the differential-difference equation is put in a traveling frame of reference, the coefficients of a candidate polynomial solution in tanh are solved for. The resulting traveling wave solutions are tested by substitution into the original differential-difference equation.
The system of differential-difference equations must be polynomial. Solutions are polynomial in tanh.
The average run time of 16 cases (including the Toda, Volterra, and Ablowitz-Ladik lattices) is 0.228 seconds with a standard deviation of 0.165 seconds on a 2.4GHz Pentium 4 with 512 MB RAM running Mathematica 4.1. The running time may vary considerably, depending on the complexity of the problem.
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