逐次逼近摄动法及其在力学中的应用

Progressively Approaching Perturbation Method and Its Application in Mechanics

提出逐次逼近摄动法，将预估的零级近似解逐渐加以修正，使之逐渐逼近于其真实解。有非线性问题的算例。算例表明，解法的精度和其它奇异摄动解法（如L—P法）的基本相同，但方法允许进行一次选代，使其精度更加提高。按照方法，可求得任一级近似解，其精度逐级提高，计算过程也很简便。

In this paper, the author proposes the progressiuely approaching perturbation method. Weprogressively correct the pro judged zeroth approximate solution in order that it progressiuely approachesthe real solution. Two calculating examples of nonlinear problems are presented. Calculating examplesshow that the accuracy of this method is basically the same as that of the other singular perturbationmethods (for example, the L-P method). But still we may use the repeated substitution method in order toimprove the accuracy of the solution. According to the method of this paper, we may obtain any orderapproximate solution and its accuracy is improved order by order. Moreover, the calculating process of themethod of this paper is quite simple.