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Numerical solutions of the GEW equation using MLS collocation method

Author

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  • Ayşe Gül Kaplan

    (Mathematics Department, Osmaniye Korkut Ata University, Osmaniye 80000, Turkey)

  • Yılmaz Dereli

    (Mathematics Department, Anadolu University, Eskişehir 26470, Turkey)

Abstract

In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known L2, L∞ error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.

Suggested Citation

  • Ayşe Gül Kaplan & Yılmaz Dereli, 2017. "Numerical solutions of the GEW equation using MLS collocation method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(01), pages 1-23, January.
    • Handle: RePEc:wsi:ijmpcx:v:28:y:2017:i:01:n:s0129183117500115
    DOI: 10.1142/S0129183117500115
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