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Modified simple equation method for nonlinear evolution equations. (English) Zbl 1201.65119
Summary: This paper reflects the implementation of a reliable technique which is called modified simple equation method (MSEM) for solving evolution equations. The proposed algorithm has been successfully tested on two very important evolution equations namely Fitzhugh-Nagumo equation and Sharma-Tasso-Olver equation. Numerical results are very encouraging.

65L05Initial value problems for ODE (numerical methods)
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34A34Nonlinear ODE and systems, general
65M70Spectral, collocation and related methods (IVP of PDE)
35Q92PDEs in connection with biology and other natural sciences
35Q40PDEs in connection with quantum mechanics
Full Text: DOI
[1] Abdou, M. A.; Soliman, A. A.: New applications of variational iteration method, Physica D 211, No. 1 -- 2, 1-8 (2005) · Zbl 1084.35539 · doi:10.1016/j.physd.2005.08.002
[2] Bekir, A.; Boz, A.: Exact solutions for nonlinear evolution equation using exp-function method, Physics letters A 372, 1619-1625 (2008) · Zbl 1217.35151 · doi:10.1016/j.physleta.2007.10.018
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[8] Shang, Y.; Qin, J.; Huang, Y.; Yuan, W.: Abundant exact and explicit solitary wave and periodic wave solutions to the Sharma -- Tasso -- Olver equation, Applied mathematics and computation 202, No. 2, 532-538 (2008) · Zbl 1151.65076 · doi:10.1016/j.amc.2008.02.034
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