基于二分法的局部常化单摆问题的N次延拓

通过引入二分法和残差，将近似求解单摆问题的局部常化法进行N次延拓，精确定量地求解N次常化系数，并利用残差比较了相关文献中的各个近似公式之间的精度．结果表明．通过二分法求得的一次常化系数优于文献给出的参考值且残差也能很好地反映各个近似解与精确解的偏离程度．

Nth Extension About Partial Normalization Method on Single Pendulum Based on Dichotomy

By introducing the concept of dichotomy and residuals, this study attempted to extend N times on partial normalization method which can approximately solve single pendulum problem to quantitatively and preciously solve the Nth partial normalization coefficients. In addition, some normalization coefficients were given and finally the pre- cisions of approximate formulas from the references were compared by using residuals. It turned out that first order partial normalization coefficient via dichotomy is superior to the reference value and the residuals can well reflect the degree of derivation between approximate solution and exact solution.