求解一维定常对流扩散反应方程的混合型紧致差分格式

借助显式紧致格式和隐式紧致格式的思想,基于截断误差余项修正,并结合原方程本身,构造出了一种求解一维定常对流扩散反应方程的高精度混合型紧致差分格式.格式仅用到三个点上的未知函数值及一阶导数值,而一阶导数值利用四阶Pade格式进行计算,格式整体具有四阶精度.数值实验结果验证了格式的精确性和可靠性.     

线性传输方程的几种数值格式的比较

本文研究了线性传输方程的数值计算问题.利用Godunov格式、Entropy格式、Ultra-bee格式和Entropy-Ultra-bee格式对线性传输方程进行了数值计算,获得了相应的数值结果.数值实验结果表明Entropy-Ultra-bee格式结合了Entropy格式和Ultra-bee格式的优点,在整个计算区域都有比较高的分辨率,而且没有出现非物理振荡.     

守恒型双曲方程的中心差分TVD格式研究

研究了如何利用迎风格式的耗散性构造中心差分ＴＶＤ格式的方法，给 相应的定理，构造出新的耗散表达式。新格式既保留了二阶中心差分格式灵活方便的优点，又吸收了迎风格式耗散项比较精细的特点，同时具有ＴＶＤ性质，使得新格式具有较同的激波分辨率。     

解三维热传导方程的一族对称含参数高精度的显式差分格式

对求解三维热传导方程利用待定参数法构造出一族对称的含参数的，截断误差为Ｏ（Δｔ＾１＋Δｘ＾４＋Δｙ＾４＋Δｚ＾４）的便于计算的三层显格式，并讨论了其条件稳定性。     

关于Jain的隐式迭代法的注

本文利用嵌入法思想构造了一类求解非线性方程组的隐式迭代法，分析了方法的收敛阶，给出了具体的计算格式，最后的计算结果表明了方法的有效性．     

粘性流动有限差分计算的新策略 *

对粘性流动计算 ,提出有限离散单元流动的流体分析 (理论 )和耦合离散流体理论(CDFT)的差分格式 .利用CDFT差分格式计算Burgers方程和计算激波边界层干扰流动的数值实验表明 :对计算精度和计算效率的提高 ,CDFT格式比提高常用差分格式 (即离散流体力学方程得到的格式 )精度和改进常用格式形式等更有效 ,且运算量小 .     

Lax-Wendroff差分格式和Rnsanov差分格式的比较

本文主要对二维不稳定流动绕障碍物问题用二阶精度的Lax-Wendroff格式计算,对此格式的边界和拐角也写出了差分格式。 对同样问题用一阶的Rnsanov格式进行了计算,把两者的结果和实验作了比较,并画出了数值计算的等压线,把两者数值计算结果和典型问题[1]进行比较,介绍这二种方法的改进[7][10]。     

对流扩散方程的数值计算

本文研究了对流扩散方程的一种并行格式.利用一组saul'yev型非对称格式进行二次构造,分别得到了一类并行GE格式和GEL、GER格式;进一步推广,得到绝对稳定的交替分组显式AGE格式,并用数值例子检验AGE格式的数值计算效果.     

一类非自共轭非线性Schroedinger方程的三层差分格式

本文对一类非自共轭非线性Schroedinger方程提出了一种三层差分格式，并证明了该格式的收敛性与稳定性，这种格式不需叠代，故计算速度比C－N格式快，数值计算结果表明，该格式是有效的和可靠的。     

一类带波动算子的非线性Schrodinger方程的一个守恒差分格式

该文对一类带波动算子的非线性Ｓｃｈｒ¨ｏｄｉｎｇｅｒ（ＮＬＳ）方程提出了一个守恒的差分格式，证明了该格式的收敛性和稳定性．数值计算结果表明，该格式对网比不敏感，具有很好的守恒性，并且比文［１］中的不守恒格式提高了计算效率．     

Product numerical range in a space with tensor product structure

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.     

基于人工鱼群算法求任意函数的数值积分

将不等距离分割方法与人工鱼群算法相结合,提出一种基于人工鱼群算法求任意函数数值积分的方法,该方法除能计算通常意义下任意函数的定积分外,还能计算奇异函数积分、振荡函数积分以及原函数不易求得的被积函数的积分.最后给出几个数值积分算例,并与传统数值积分方法作了比较,仿真结果分析表明,该算法十分有效,能够快速有效地获得任意函数的数值积分值.     

A numerical approach for solving an extended Fisher-Kolomogrov-Petrovskii-Piskunov equation

In the present paper a numerical method, based on finite differences and spline collocation, is presented for the numerical solution of a generalized Fisher integro-differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed-form difference scheme. A number of test examples are solved to assess the accuracy of the method. The numerical solutions obtained, indicate that the approach is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods. Convergence and stability of the scheme have also been discussed.     

带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式

基于已有的针对单侧正规化回火分数阶扩散方程的三阶拟紧算法,将该算法的思想应用于带漂移的单侧正规化回火分数阶扩散方程的数值模拟,并结合Crank-Nicolson方法导出数值格式.证明了数值格式的稳定性与收敛性,且数值格式的时间收敛阶和空间收敛阶分别是二阶和三阶.通过数值试验验证了数值格式的有效性和理论结果.     

Smooth factorizations of matrix valued functions and their derivatives

Summary In this paper we study the numerical factorization of matrix valued functions in order to apply them in the numerical solution of differential algebraic equations with time varying coefficients. The main difficulty is to obtain smoothness of the factors and a numerically accessible form of their derivatives. We show how this can be achieved without numerical differentiation if the derivative of the given matrix valued function is known. These results are then applied in the numerical solution of differential algebraic Riccati equations. For this a numerical algorithm is given and its properties are demonstrated by a numerical example.     

Recovering the local volatility in Black–Scholes model by numerical differentiation

In this article, a numerical method for recovering the local volatility in Black–Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The convergent analysis and numerical examples are also given. It shows that our method is efficient and stable.     

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.     

A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation

In this paper, a numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection diffusion equation is presented. The convergence and stability of the numerical approximation method are discussed by a new technique of Fourier analysis. The solvability of the numerical approximation method also is analyzed. Finally, applying Richardson extrapolation technique, a high-accuracy algorithm is structured and the numerical example demonstrated the theoretical results.     

The Quadratic Numerical Range of an Analytic Operator Function

We introduce a new concept of numerical range for analytic operator functions. This so-called quadratic numerical range is induced by a decomposition of the underlying Hilbert space. Like the classical numerical range of an operator function, it is not convex, it has the spectral inclusion property, and it provides resolvent estimates and estimates for the lengths of Jordan chains in boundary points having the exterior cone property. As the quadratic numerical range is contained in the numerical range, it yields tighter enclosures for the eigenvalues and the spectrum of analytic operator functions.     

Numerical pseudodifferential operator and Fourier regularization

The concept of numerical pseudodifferential operator, which is an extension of numerical differentiation, is suggested. Numerical pseudodifferential operator just is calculating the value of the pseudodifferential operator with unbounded symbol. Many ill-posed problems can lead to numerical pseudodifferential operators. Fourier regularization is a very simple and effective method for recovering the stability of numerical pseudodifferential operators. A systematically theoretical analysis and some concrete examples are provided.