Periodic wave solution of a second order nonlinear ordinary differential equation by Homotopy analysis method

Hao Song, Longbin Tao

Abstract


The periodic wave solution of a second order nonlinear ordinary differential equation is obtained by the homotopy analysis method, an analytical, totally explicit mathematical technique. By choosing a proper auxiliary parameter, the new series solution converges very fast. The method provides us with a simple way to adjust the convergence region. Furthermore, a significant improvement of the convergence rate and region is achieved by applying Homotopy-Pade approximants. Three examples demonstrate the excellent computation accuracy and efficiency of the present HAM approach. The present method could be extended for more complicated wave equations.

References
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Keywords


Homotopy analysis method, nonlinear wave equation, periodic wave solution

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DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2434



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