摘要
提出了利用Euler小波方法求解带有Dirichlet,Neumann和Neumann-Robin型边界条件的一类Lane-Emden型微分方程数值解.借助Euler多项式解析形式,推导出Riemann-Liouville分数阶定义下Euler小波函数的分数阶积分计算公式.利用Euler小波配置法来将带有边界条件的Lane-Emden方程转为代数方程组,然后采用牛顿法进行求解,最后通过求解不同边界条件下的Lane-Emden方程,验证了Euler小波方法的准确性和有效性.数值计算结果与其他方法的计算结果和精确解进行了比较.
In the report,the Euler wavelet method which was used to solve the numerical solutions of a class of Lane-Emden equations with Dirichlet,Neumann and Neumann-Robin type boundary conditions was proposed.The analytic form of Euler polynomials was used to derive the fractional integration formula of Euler wavelet functions in the sense of Riemann-Liouville.The Euler wavelet collocation method was used to reduce the Lane-Emden equation with boundary conditions to a system of nonlinear algebraic equations,then,the Newton’s method was used for numerical solutions.Several examples of the Lane-Emden equation with different types of boundary conditions were provided to demonstrate the accuracy and efficiency of the proposed method.The numerical results were compared with the results obtained by other techniques and the exact solution.
作者
徐志刚
周凤英
Xu Zhigang;Zhou Fengying(School of Science,East China University of Technology,Nanchang 330013,China)
出处
《海南大学学报（自然科学版）》
CAS
2020年第3期207-215,共9页
Natural Science Journal of Hainan University
基金
国家自然科学基金(11601076)
江西省自然科学基金(2020BABL201006)
东华理工大学博士科研启动金(DHBK2019213)。
