常微分方程光滑性解的求取过程改进分析

Analysis of Calculating Process Improvement for Ordinary Differential Equations Smooth Solution

为了优化常微分方程光滑性解的求取过程,提出一种拉普拉斯变换以及小波匹配的常微分方程光滑性解求取方法,采用拉普拉斯变换方法将常微分方程(组)转换成复变数的代数方程(组),通过一些代数运算和拉普拉斯变换表,获取常微分方程的初始光滑性解,将任意函数展开成小波基函数,通过快速离散小波转换技术,塑造常微分方程的近似光滑性解,在运算过程中,在小波展开层次以及自变量区间,使用多层自适应以及多区间自适应方法,对长时间问题进行分段求解,保证在每个时间段上达到所要求的数值精度,提高光滑性解求解的效率和精度。数值实验结果说明,所提方法求解常微分方程光滑解的精度以及长时间性态都优于传统的时间推进方法。

Smoothness in order to optimize the differential equations of calculating process, put forward akind of Laplace transform and the wavelet matching calculate the smoothness of ordinary differentialequation solution method and Laplace transform method is used to convert ordinary differential equation（group） to the algebraic equation （group） of complex variable, by some algebraic operation and Laplacetransform table, get initial smoothness solution of ordinary differential equations, the arbitrary functionexpansion ChengXiaoBo basis function, through the fast discrete wavelet transform technology, shape thesmoothness of approximate solution of ordinary differential equations, in the process of operation, inwavelet levels, as well as the independent variable interval, using multilayer adaptive method, adaptiveand interval section to solve the problems of the long time, ensure in each time period to achieve therequired accuracy and smoothness of solution to solve and improve efficiency and accuracy. The result ofnumerical experiment shows that the proposed method for solving ordinary differential equations ofsmooth solution accuracy and timeliness is better than the traditional state long time propulsion method.