一类非线性投影方程解的扰动迭代算法及其收敛性

在Hilbert空间中讨论了一类非线性投影方程解的扰动迭代算法及其收敛性分析．     

用遗传算法解算病态方程

对应用遗传算法解决病态方程问题进行了探讨。利用拟合法而不是通过法方程求解参数，从而避免了法方程系数求逆，使病态方程的解答有了较好的结果。通过模拟计算并和其他方法进行比较，证明该方法是可行的和有效的。     

Lienard方程零解渐近稳定性的一个弱条件

研究Liemrd方程零解的渐近稳定性.在Liapunov函数Ⅴ满足dV/dt≤0的情况下,给出了进一步判断其渐近稳定的一个条件.     

The Convergence of Newton–Raphson Iteration with Kepler's Equation

Conway (Celest. Mech. 39, 199–211, 1986) drew attention to the circumstance that when the Newton–Raphson algorithm is applied to Kepler's equation for very high eccentricities there are certain apparently capricious and random values of the eccentricity and mean anomaly for which convergence seems not to be easily reached when the starting guess for the eccentric anomaly is taken to be equal to the mean anomaly. We examine this chaotic behavior and show that rapid convergence is always reached if the first guess for the eccentric anomaly is π. We present graphs and an empirical formula for obtaining an even better first guess. We also examine an unstable situation where iterations oscillate between two in correct results until the instability results in sudden convergence to the unique correct solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Corrections to Solar Thermal Structure when a Turbulent Magnetic Field is Included

Correction of non-ideal effect due to a magnetic fluctuating tensor is derived from the ideal MHD equations. The inclusion of a magnetic turbulent field leads to modifications of the hydrostatic equilibrium equation and thermodynamical variables such as the temperature T, the adiabatic exponent γ, the adiabatic temperature gradient △↓ad and the temperature gradient △↓. In particular, the modifications in the adiabatic and radiative temperature gradients will result in a change in the Schwarzchild criterion, hence in the location of the base of the convective zone. Incorporating the modifications, we construct a modified thermodynamical equilibrium structure of the Sun.     

Extension of the solution of Kepler's equation to high eccentricities

The classic Lagrange's expansion of the solutionE(e, M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627 ... <e<1. The solutionE(e, M) is developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functionsJ _n (ne). The expansion is convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is a positive real number, which is calculated numerically.     

研究Lienard方程闭轨线的一种方法

结合实例分析说明 Filippov变换在研究 Lienard方程不存在闭轨线时的运用方法     

圆透视曲线类型及相对视点画面的位置的分析

圆曲线的透视根据圆曲线相对视点、画面的位置不同,可以有五种结果,分别为直线、圆、椭圆、双曲线、抛物线     

LNAPL在二维含水介质中运移规律的研究

为研究LNAPL （轻质非水相液体）污染物在均匀含水介质中的运移规律,本文建立微元模型推导出LNAPL在均匀含水介质中的对流--弥散方程。针对不同的介质模型,对二维对流--弥散方程运用差分法进行数值模拟,求其数值解。分析LNAPL污染物的运移特征,得出在均匀介质和非均匀层状介质中运移规律： LNAPL污染物在含水介质中的运移规律遵循对流--弥散方程,介质的弥散系数是影响LNAPL污染物运移的主要因素。     

Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane–Emden type

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane–Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane–Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.