《同文算指》中的方程解法

《同文算指》中包括二项二次和三次方程、二次和三次一般方程、高次方程等,李之藻采用传统数学的表述方式描述西方数学的方程解法,综合中西数学说明求解方程时根的位数、次商的求法,并给出没有整数根的方程解法.从方程解法的分析发现《同文算指》是中国学者力图会通中西数学的一部数学著作.     

An analytical approximation for solving nonlinear Blasius equation by NHPM

In this article, an analytic approximation to the solution of Blasius equation is obtained by using a new modification of homotopy perturbation method. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The comparison with Howart's numerical solution shows that the new homotopy perturbation method is an effective mathematical method with high accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Derivative swift-Hohenberg方程的初边值问题解的存在性

运用压缩影射原理证明了DS-H方程的初边值问题的局部解的存在性和唯一性.     

A “Discretization” Technique for the Solution of ODEs II

A functional analytic technique was recently presented for finding discrete equivalent counterparts of initial value problems of ODEs and obtaining their real analytic solutions. In the current paper, this technique is extended to boundary value problems of ODEs and to the complex solutions of ODEs. In order to demonstrate this technique, it is applied to the classic Blasius problem of fluid mechanics. Apart from its real solution, its complex solution is also studied. The obtained results indicate that the complex Blasius function exhibits an oscillatory behavior and strengthen a conjecture regarding its singularities in the complex plane.     

Asymptotic suction profiles for the Blasius and Sakiadis flow with constant and variable fluid properties

A theoretical study of the effect of variable fluid properties on the Blasius and Sakiadis flow with uniform suction at the asymptotic state is presented in this paper. The investigation concerns air and water taking into account the variation of their physical properties with temperature. Velocity and temperature profiles are presented as well as values of the displacement thickness, momentum thickness, shape factor, wall shear stress and Nusselt number for different temperatures of the plate and the ambient fluid. It is found that the nondimensional displacement thickness, momentum thickness, shape factor, absolute wall shear stress and Nusselt number are identical in both Blasius and Sakiadib flow at the asymptotic state for a fluid with constant properties. The same is valid for any fluid with variable properties if the temperature boundary conditions are the same in Blasius and Sakiadis flow.     

二维边界层方程的迭代求解

针对二维边界层方程,提出了分析积分迭代法.首先将该方法应用于Blasius方程和Falkner-Skan方程的求解,数值计算结果稳定,计算精度高;然后对外部有势流不能达到自相似要求、必须二维求解的二维层流边界层问题,在分析积分迭代法中加上计算力学的松弛迭代法,形成了一套有效的算法.数值结果表明该方法用于层流边界层的计算是很有效的.     

A non-iterative transformation method for Blasius equation with moving wall or surface gasification

We define a non-iterative transformation method for Blasius equation with moving wall or surface gasification. The defined method allows us to deal with classes of problems in boundary layer theory that, depending on a parameter, admit multiple or no solutions. This approach is particularly convenient when the main interest is on the behaviour of the considered models with respect to the involved parameter. The obtained numerical results are found to be in good agreement with those available in the literature.     

二维双曲型方程动边界问题有限元逼近格式和数值分析

1 引言 物理实际中,许多振动的传播过程,如弦振动、弹性杆纵向振动过程中的位移,理想高频传输线上的电压和电流,声波传播中的声压速度势以及电磁波等,都满足双曲型方程。关于     

非线性Blasius方程求解的一种新算法

通过一半无限大平板的不可压缩的两维稳定流是一个典型的工程问题,被称为边界层流问题.它是一个由三阶非线性微分方程描述的边值问题,其微分方程称为Blasius方程.首先将该边值问题转化为一对初值问题,然后用状态方程直接积分法和Taylor级数展开法对这对初值问题进行求解.与其它算法相比,具有算法简单,精度高的优点.