双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Ku...双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较,验证了方法的有效性,数据结果的误差与其他方法相比有较高的精确度。Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.展开更多
在求解奇异摄动两点边值问题时,本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数,利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动...在求解奇异摄动两点边值问题时,本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数,利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动扩散反应问题、奇异摄动对流扩散反应问题这两个算例的研究,表明基于Chebyshev点的B样条配置法与等距节点下的B样条配置法相比,前者具有高精度和高效率的优势。In solving the singular perturbation two-point boundary value problems, this paper constructs a Chebyshev B-spline collocation method. This method uses cubic B-spline functions as basis functions and utilizes the Chebyshev point as the configuration point to solve the equation directly. The specific steps in the implementation of the method and several details that need to be noted are discussed in the paper. Through the study of two arithmetic cases, namely, the singular regent diffusion response problem and the singular regent convection diffusion response problem, it is shown that the Chebyshev B-spline collocation method has the advantages of high accuracy and high efficiency as compared with the B-spline configuration method under equidistant nodes.展开更多
语篇意识是概要写作的起点,理解写作意图有助于学生识别语篇类型和模式,把握主旨,梳理结构,进而确定概要写作的核心。借助语篇分析和衔接理论,将高中英语概要写作的教学路径划分为写前(辨识体裁和模式等)、写中(确立主题句等)、写后(自...语篇意识是概要写作的起点,理解写作意图有助于学生识别语篇类型和模式,把握主旨,梳理结构,进而确定概要写作的核心。借助语篇分析和衔接理论,将高中英语概要写作的教学路径划分为写前(辨识体裁和模式等)、写中(确立主题句等)、写后(自我评价与修改)三个阶段。以概要写作“Dealing with One Missed Workout”作为教学素材,分析教学流程和设计思路,并给出相应的教学建议,以促进学生概要写作能力和思维能力的发展。展开更多
文摘双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较,验证了方法的有效性,数据结果的误差与其他方法相比有较高的精确度。Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.
文摘在求解奇异摄动两点边值问题时,本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数,利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动扩散反应问题、奇异摄动对流扩散反应问题这两个算例的研究,表明基于Chebyshev点的B样条配置法与等距节点下的B样条配置法相比,前者具有高精度和高效率的优势。In solving the singular perturbation two-point boundary value problems, this paper constructs a Chebyshev B-spline collocation method. This method uses cubic B-spline functions as basis functions and utilizes the Chebyshev point as the configuration point to solve the equation directly. The specific steps in the implementation of the method and several details that need to be noted are discussed in the paper. Through the study of two arithmetic cases, namely, the singular regent diffusion response problem and the singular regent convection diffusion response problem, it is shown that the Chebyshev B-spline collocation method has the advantages of high accuracy and high efficiency as compared with the B-spline configuration method under equidistant nodes.
文摘语篇意识是概要写作的起点,理解写作意图有助于学生识别语篇类型和模式,把握主旨,梳理结构,进而确定概要写作的核心。借助语篇分析和衔接理论,将高中英语概要写作的教学路径划分为写前(辨识体裁和模式等)、写中(确立主题句等)、写后(自我评价与修改)三个阶段。以概要写作“Dealing with One Missed Workout”作为教学素材,分析教学流程和设计思路,并给出相应的教学建议,以促进学生概要写作能力和思维能力的发展。
