最速降线问题的3-尺度正交Euler小波方法  

Numerical Solution for Brachistochrone Problem Using 3-scale Orthogonal Euler Wavelet Method

作　　者：朱婷 许小勇 朱合欢 ZHU Ting;XU Xiao-yong;ZHU He-huan(School of Science,East China University of Technology,Nanchang 330013,China)

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《数学的实践与认识》2022年第3期158-166,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11601076);江西省自然科学基金项目(20202BABL201006);东华理工大学博士科研启动项目(DHBK2019213)。

摘　　要：针对Euler小波非正交的缺点,提出了3-尺度正交Euler小波.利用施密特正交化过程将Euler多项式正交归一化,再根据小波的构造方法得到3-尺度正交Euler小波.分析了3-尺度正交Euler小波级数的收敛性与误差估计,利用Laplace变换推导了Euler小波的Riemann-Liouville分数阶积分公式.结合Lagrange乘数法将最速降线问题转化为代数方程组求解,数值结果验证了算法的有效性和高精度性.Aiming at the shortcomings of non-orthogonal Euler wavelets,a 3-scale orthonormal Euler wavelet is proposed.The Euler polynomials are normalized by Schmidt orthogonalization process,and then the 3-scale orthonormal Euler wavelets are obtained according to the construction method of wavelets.The convergence and error estimation of the 3-scale orthonormal Euler wavelet series are analyzed,and the Riemann-Liouville fractional integral formula of Euler wavelet is derived using Laplace transform.Combining with Lagrange multiplier method,the brachistochrone problem is transformed into the algebraic equations.Numerical results show the effectiveness and high accuracy of the algorithm.

关 键 词：最速降线问题 3-尺度正交Euler小波 拉普拉斯变换 Riemann-Liouville分数阶积分 LAGRANGE乘数法 

分 类 号：O175[理学—数学]