短波近似的保辛算法

WKBJ短波近似是最常用的有效求解方法之一。保守体系的微分方程可用Hamilton体系的方法描述,其特点是保辛。保辛给出保守体系结构最重要的特性。但WKBJ短波近似却未曾考虑保辛的问题。WKBJ近似可用自变量坐标变换,然后再给出其保辛摄动。数值例题展示了本文变换保辛算法的有效性。

Symplectic conservative integration for short-wave approximation

All approximations for a conservative system should be symplectic conservative.The traditional perturbation approaches are based on the Taylor series expansion which uses additional operation.The addition for a transfer symplectic matrix is not symplectic conserved,however,the symplectic matrices are conserved under multiplication.The symplectic conservative perturbation for a conservative system can use the canonical transformation method.However,the well-known WKBJ short wave-length approximation is not symplectic conservative.The former paper7] has not taken the coordinate transformation into consideration,more steps of integration are necessary.The method of coordinate transformation and the polynomial approximation of mixed energy density are applied in this paper,and then the solution of unknown state vector is solved,which needs far fewer steps of integration.Numerical results demonstrate the effectiveness of the present method.