自共轭常微分方程奇异摄动问题一致收敛的差分格式

本文对自共轭常微分方程奇异摄动问题,构造一族带拟合因子的差分格式,用不同于[1]的方法,通过对格式截断误差的分析,给出差分格式解一致收敛于微分方程解的充分条件;由此提出几个具体的差分格式,在较弱的条件下,给出较高的一致收敛阶,并将它们应用于例子,给出数值结果.     

二阶非线性q-差分微分方程两点边值问题两个迭代正解的存在性*

研究了二阶非线性q-差分微分方程两点边值问题,给出了系统两个正解存在的充分条件. 与其他文献中使用的不动点定理不同,文章不仅证明了该系统正解的存在性, 而且还利用单调迭代技巧给出了逼近正解的迭代格式.     

有红利美式看跌期权定价的Crank-Nicolson有限差分法

本文基于B-S微分方程,采用Crank-Nicolson差分格式(简称C-N差分格式)求解支付固定红利的美式看跌期权价值,给出实证分析,并对C-N差分格式和隐含的差分格式进行了比较.结果表明,用C-N差分格式可以得到更加精确、有效的数值解.     

一类多维非线性反应扩散方程有限差分格式的稳定性问题(英文)

本文研究了一类多维线性反应扩散方程差分格式的稳定性.利用量未知元方法,建立了具有增量未知元的有限差分格式;然后利用非线性Galerkin方法,得到该差分格式的稳定性条件.通过对该格式的稳定性分析,说明和经典的差分格式的稳定性相比较,带有增量未知元的有限差分格式的稳定性得到了提高.     

广义非线性Schr(o)dinger方程的一个新的守恒差分格式

对广义非线性Schr(o)dinger方程提出了一种新的差分格式.揭示了该差分格式满足两个守恒律,并证明该格式的收敛性和稳定性.数值实验结果表明,新的差分格式优于Crank-Nicolson格式以及Zhang Fei等人提出的格式.     

广义非线性Schringer方程的一个新的守恒差分格式

对广义非线性Schro。d inger方程提出了一种新的差分格式.揭示了该差分格式满足两个守恒律,并证明该格式的收敛性和稳定性.数值实验结果表明,新的差分格式优于C rank-N ico lson格式以及Zhang Fei等人提出的格式.     

小参数常微分方程守恒型差分格式的一致收敛性

本文考虑自共轭常微分方程奇异摄动边值问题,构造一族带拟合因子的差分格式,给出差分格式解一致收敛于微分方程解的充分条件,由此提出几个具体格式,在条件较弱的情况下,给出较高的一致收敛阶。     

解抛物型方程的一族高精度隐式差分格式

构造了求解一维抛物型方程的一族高精度隐式差分格式.首先,推导了抛物型方程解的一阶偏导数在特殊节点处的一个差分近似式,利用该差分近似式和二阶中心差商近似式用待定系数法构造了一族隐式差分格式,通过选取适当的参数使格式具有高阶截断误差;然后,利用Fourier分析法证明了当r大于1/6时,差分格式是稳定的.最后,通过数值试验将差分格式的解与具有同样精度的其它差分格式的解和精确解进行了比较,并比较了差分格式与经典差分格式的计算效率.结果说明了差分格式的有效性.     

声波方程高阶差分方法数值模拟结果研究

首先,给出了声波方程时空域高阶差分格式.证明了差分格式在时间上是二阶精度,在空间上最高可以达到2M精度.其次,对该高阶差分格式优缺点评价,新的差分格式是一种关于一个方向上所用到的临近网格节点数目一半的可变长度的差分算子,为不同精度需求提供了灵活可变的差分算子公式.另外一种意义上说,新的差分格式是依赖于频率的,同一种差分格式对于不同频率的震源,其频散的程度也不一样,因此只有采用了合适的差分形式才能够达到最好的效果.最后,给出了一系列数值模拟实例,验证了文中所得到的结论.     

KdV-Burgers方程的一类新本性并行差分格式北大核心CSCD

KdV-Burgers方程作为湍流规范方程,具有深刻的物理背景,其快速数值解法具有重要的实际应用价值.针对KdV-Burgers方程,提出了一种新型的并行差分格式.基于交替分段技术,结合经典Crank-Nicolson(C-N)格式、显格式和隐格式,构造了混合交替分段Crank-Nicolson(MASC-N)差分格式.理论分析表明MASC-N格式是唯一可解、线性绝对稳定和二阶收敛的.数值试验表明,MASC-N格式比C-N格式具有更高的精度和效率.与ASE-I和ASC-N差分格式相比,MASC-N并行差分格式有最好的性能.表明该文的MASC-N并行差分方法能有效地求解KdV-Burgers方程.     

Burgers方程的区域分裂并行格式

1引言 Burgers方程可作为N-S方程的简单形式,这是因为它不仅具有N-S方程的一些特性,而且数值求解方法也相近,因此,对Burgers方程的数值方法的研究具有一定的实际意义.为了在并行计算机上求解Burgers方程,已有不少文章提出了并行差分格式,如组显式方法([1]-[4])、交替分段隐格式[5],这些格式均可归结为交替型的并行格式.     

一类非线性反应-扩散方程有限差分格式的稳定性研究

In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.     

The effect of a parameter in a boundary condition on the stability of difference schemes

A nonlocal difference scheme for the heat conduction equation with a real parameter γ > 1 or γ < 0 in the boundary condition is considered. Thus, the analysis of this problem is generalized to all real values of the parameter in the boundary condition. The spectrum of the spatial operator of the scheme is studied. The results obtained are used to formulate a stability criterion for the difference scheme. The case γ = ?1 proves to be special, because the system of eigenfunctions of the operator does not form a basis in the space of grid functions.     

Numerical solutions of diffusion mathematical models with delay

In this paper an explicit numerical difference scheme for mixed problems for the delay diffusion equation is proposed, as a generalization of the classic difference scheme for the diffusion problem. A sufficient condition for the asymptotic stability of the new scheme is proved. Consistence, convergence and some properties of stability for this scheme are studied. Illustrative examples of numerical results are also included.     

To the theory of asymptotically stable second-order accurate two-stage scheme for an inhomogeneous parabolic initial-boundary value problem

An asymptotically stable two-stage difference scheme applied previously to a homogeneous parabolic equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial condition is extended to the case of an inhomogeneous parabolic equation with an inhomogeneous Dirichlet boundary condition. It is shown that, in the class of schemes with two stages (at every time step), this difference scheme is uniquely determined by ensuring that high-frequency spatial perturbations are fast damped with time and the scheme is second-order accurate and has a minimal error. Comparisons reveal that the two-stage scheme provides certain advantages over some widely used difference schemes. In the case of an inhomogeneous equation and a homogeneous boundary condition, it is shown that the extended scheme is second-order accurate in time (for individual harmonics). The possibility of achieving second-order accuracy in the case of an inhomogeneous Dirichlet condition is explored, specifically, by varying the boundary values at time grid nodes by O(τ ²), where τ is the time step. A somewhat worse error estimate is obtained for the one-dimensional heat equation with arbitrary sufficiently smooth boundary data, namely, $O\left( {\tau ^2 \ln \frac{T} {\tau }} \right) $ , where T is the length of the time interval.     

Numerical bifurcation of a delayed diffusive food‐limited model with Dirichlet boundary condition

This paper studies the Neimark–Sacker bifurcation of a diffusive food‐limited model with a finite delay and Dirichlet boundary condition by the backward Euler difference scheme, Crank‐Nicolson difference scheme, and nonstandard finite‐difference scheme. The existence of Neimark‐Sacker bifurcation at the equilibrium is obtained. Our results show that Crank‐Nicolson and nonstandard finite‐difference schemes are superior to the backward Euler difference scheme under the means of describing approximately the dynamics of the original system. Finally, numerical examples are provided to illustrate the analytical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability of Rothe difference scheme for the reverse parabolic problem with integral boundary condition

In this paper, we study the approximation of reverse parabolic problem with integral boundary condition. The Rothe difference scheme for an approximate solution of reverse problem is discussed. We establish stability and coercive stability estimates for the solution of the Rothe difference scheme. In sequel, we investigate the first order of accuracy difference scheme for approximation of boundary value problem for multidimensional reverse parabolic equation and obtain stability estimates for its solution. Finally, we give numerical results together with an explanation on the realization in one- and two-dimensional test examples.     

On the stable difference scheme for source identification nonlocal elliptic problem

Approximation of source identification problem for elliptic equation with integral-type nonlocal condition is discussed. The first order of accuracy difference scheme for elliptic nonlocal identification problem is studied. By using spectral resolution of a self-adjoint operator, we establish stability inequalities for solution of constructed scheme. Subsequently, the difference scheme for approximate solution of multidimensional boundary value problem with integral-type nonlocal and first kind boundary conditions is investigated on stability. Numerical test examples are presented.     

A completely conservative difference scheme of gas dynamics in orthogonal curvilinear coordinates

A completely conservative difference scheme in Eulerian curvilinear orthogonal coordinates is proposed for calculating discontinuous gas-dynamic flows on sufficiently coarse grids. The stability of the linear approximation of the proposed scheme is analyzed. Courant's condition provides a stability condition for this scheme.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 9–15, 1986.