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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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A34 Nonlinear ordinary differential equations and systems
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35Q40 PDEs in connection with quantum mechanics
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References:

[1] Abdou, M. A.; Soliman, A. A., New applications of variational iteration method, Physica D, 211, 1-2, 1-8 (2005) · Zbl 1084.35539
[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
[3] Chen, A., New kink solutions and soliton fission and fusion of Sharma-Tasso-Olver equation, Physics Letters A, 374, 23, 2340-2345 (2010) · Zbl 1237.37047
[7] Pan, J.-T.; Chen, W.-Z., A new auxilliary equation method and its application to the Sharma-Tasso-Olver equation, Physics Letters A, 373, 35, 3118-3121 (2009) · Zbl 1233.34004
[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, 2, 532-538 (2008) · Zbl 1151.65076
[9] Song, L.; Wang, Q.; Zhang, H., Rational approximation solution to the fractional Sharma-Tasso-Olver equation, Journal of Computational and Applied Mathematics, 224, 1, 210-218 (2009) · Zbl 1157.65074
[10] Wazwaz, A.-M., New solitons and kink solutions to the Sharma-Tasso-Olver equation, Applied Mathematics and Computation., 188, 2, 1205-1213 (2007) · Zbl 1118.65113
[11] Yefimova, O. Yu.; Kudryashov, N. A., Exact solutions of the Burgers-Huxley equation, Journal of Applied Mathematics and Mechanics, 68, 3, 413-420 (2004) · Zbl 1092.35084
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