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| Homotopy perturbation method for nonlinear dynamic equations based on precise integration technology |
| Revised:January 06, 2004 |
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| DOI：10.7511/jslx20056129 |
| KeyWord:homotopy perturbation method,nonlinear dynamic equations,precise integration method |
| MEI Shu-li~1 ZHANG Sen-wen~2 |
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| Abstract: |
| A new asymptotic numerical method for nonlinear dynamic equations is proposed in this paper by combining the precise integration method(PIM) with the homotopy perturbation method(HPM).For solving nonlinear dynamic equations in PIM,the nonlinear term should be expanded in Taylor series to the time parameter.The computational accuracy is sensitive to the time step if the series is truncated at the first order or second order,and if the series is truncated at the higher order,the computational format will be more complex.Correspondingly,the format derived from the homotopy perturbation method is simpler,but its applicability is limited to one or two dimensional nonlinear differential equations and the computational accuracy is lower.The new asymptotic numerical method obtained by combining above two methods possesses all their merits,that is,not only extend the applicability of the homotopy perturbation method to high dimensional nonlinear dynamic equations,but also simplify the computational format of PIM in solving nonlinear problems.The numerical example shows that the numerical accuracy and the computational efficiency of the new method is higher. |
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