求解非线性方程的一种线化和校正方法

Linearization and Correction Method for Nonlinear Problems

提出了一种拟摄动理论———线化和校正方法· 在该理论中 ,不象传统的摄动方法假设其近似解可表示成小参数的级数形式 ,而是先把方程线性化 ,再求其线化方程的解 ,然后再校正线化方程的解· 这样得到的近似解不受方程中的“参数”的影响·

A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.