Modified simple equation method for nonlinear evolution equations.

*(English)*Zbl 1201.65119Summary: 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 |

##### Keywords:

solitons; exact solutions; modified simple equation method;evolution equations; algorithm; Fitzhugh-Nagumo equation; Sharma-Tasso-Olver equation; numerical results
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\textit{A. J. Mohamad Jawad} et al., Appl. Math. Comput. 217, No. 2, 869--877 (2010; Zbl 1201.65119)

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##### References:

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