奇异摄动理论中的人工参数法及其应用

ARTIFICIAL PARAMETER METHODUSED IN SINGULARPERTURBATION PROBLEMS

  • 摘要: 为了求解无小参数的非线性方程,可以在方程里引进一人工参数,再按人工参数展开,并同时应用Lindsedt-Poincare理论即可得到其很好的近似解。本文还阐述了如何确定最佳人工参数方程,几个实例表明这种方法是比较有效的。

     

    Abstract: in order to solve a nonlinear equationwithout small parameters, it is convenient to intro-duce an artificial parameter in the equation, thenthe approximate solution can be expressed as seriesof the artificial parameter just as traditional pertur-bation techniques do.Combining it with Lindstedt-Poincare technique leads to a more convenient re-sults with good accuracy.

     

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