应用一种新的摄动方法求解数学摆的近似解析解

应用同伦技术和摄动技术,提出了一种求解数学摆的近似解析解的新摄动方法。这种方法有别于传统的摄动理论,它不依赖于小参数,而是应用同伦技术,构造一个含嵌入参数ｐ∈「０,１」的方程,然后把嵌入参数作为“小参数”。因此这种新的方法可以充分应用各种摄动方法,结果显示这种方法简单而有效,并且其一阶近似往往具有很高的精度。

A new perturbation technique and its applicationto a mathematical pendulum

A new perturbation technique is proposed, which, in contrast to the traditionalperturbation methods, does not require small parameters in the equations. In this method,according to the homotopy technique, a homotopy with an imbeding parameter isconstructed, and the imbedding parameter is considered as a "small parameter", so the pro-posed method can take the full advantages of the traditional perturbation methods. The resultreveals that the new method is very effective and simple, and it appears that even the first-ordersolution is of high accuracy.