一种求解时滞微分方程的小波方法  

A wavelet method for solving delay differential equations

作　　者：刘小靖[1] 周又和[1] 周俊[1] 

机构地区：[1]兰州大学西部灾害与环境力学教育部重点实验室,土木工程与力学学院,兰州730000

出　　处：《兰州大学学报（自然科学版）》2011年第1期87-90,96,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金青年基金项目(10802034);国家自然科学基金项目(10972094)

摘　　要：提出了一种基于小波理论的求解线性时滞微分方程的数值方法,该方法将线性时滞微分方程的解在求解区域内展开为小波尺度函数级数,再利用配点法将时滞微分方程的初值问题转化为线性代数方程组的求解问题.与传统的逐步数值积分方法相比,该方法将方程的解在求解区域内做全局小波近似,因而具有全局误差可控的优点,从而有效地克服了逐步数值积分法所固有的误差积累的缺陷,并具有很高的精度.A new numerical method based on wavelets was proposed for solving linear ordinary differential equations with time delays. In the proposed method wavelet approximation was established for the solution of time-delayed ordinary differential equations, and then the initial-value problem of time-delayed ODE was equivalently transformed to a linear algebraic equation by applying the wavelet collocation method. Because the wavelet approximation of solution is a global expression, the global error of solution can be controlled and the cumulative error eliminated, as compared with conventional step-by-step methods. The proposed method has high accuracy.

关 键 词：线性时滞微分方程 SHANNON小波 小波配点法 初值问题 高精度 

分 类 号：O241[理学—计算数学]