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1.
一类偏积分微分方程二阶差分全离散格式   总被引:1,自引:0,他引:1  
本给出了数值求解一类偏积分微分方程的二阶全离散差分格式.采用了Crank-Nicolson格式;积分项的离散利用了Lubieh的二阶卷积积分公式;给出了稳定性的证明,误差估计及收敛性的结果.  相似文献   

2.
一类非线性偏积分微分方程二阶差分全离散格式   总被引:1,自引:0,他引:1  
给出了数值求解一类非线性偏积分微分方程的二阶全离散差分格式.采用了二阶向后差分格式,积分项的离散利用了Lubich的二阶卷积求积公式,给出了稳定性的证明、误差估计及收敛性的结果.  相似文献   

3.
本文给出了数值求解一类偏积分微分方程的一阶差分全离散格式。时间方向采用了一阶向后差分格式,空间方向采用二阶差分格式,给出了稳定性的证明,误差估计及收敛性的结果,并给出了数值例子。  相似文献   

4.
本文给出了数值求解一类带弱奇异核偏积分微分方程的二阶差分空间半离散格式;借助于Laplace变换及Parseval等式,得到了全局稳定性的证明.  相似文献   

5.
偏积分微分方程产生于许多科学与工程领域,数值求解此类问题具有重要应用.本文给出了数值求解一类长时间偏积分微分方程的二阶差分空间半离散格式.借助于Laplace变换及Parseval等式,给出了全局稳定性的证明、误差估计及全局收敛性的结果.  相似文献   

6.
李丽  许传炬 《数学研究》2008,41(2):132-141
考察一类带幂次非线性项的Schrodinger方程的Dirichlet初边值问题,提出了一个有效的计算格式,其中时间方向上应用了一种守恒的二阶差分隐格式,空间方向上采用Legendre谱元法.对于时间半离散格式,证职了该格式具有能量守恒性质,并给出了L^2误差估计,对于全离散格式,应用不动点原理证明了数值解的存在唯一性,并给出了L^2误差估计.最后,通过数值试验验证了结果的可信性.  相似文献   

7.
腾飞  罗振东 《计算数学》2014,36(2):205-214
首先给出二维非饱和土壤水流方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN广义差分格式,并给出误差分析,最后用数值例子验证全离散化CN广义差分格式的优越性.这种方法能提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且该方法可以绕开对空间变量的半离散化广义差分格式的讨论,使得理论研究更简便.  相似文献   

8.
二维半线性反应扩散方程的交替方向隐格式   总被引:2,自引:0,他引:2  
吴宏伟 《计算数学》2008,30(4):349-360
本文研究一类二维半线性反应扩散方程的差分方法.构造了一个二层线性化交替方向隐格式.利用离散能量估计方法证明了差分格式解的存在唯一性、差分格式在离散H~1模下的二阶收敛性和稳定性.最后给出两个数值例子验证了理论分析结果.  相似文献   

9.
该文将研究二维分数阶发展型方程的正式的二阶向后微分公式(BDF)的交替方向隐式(ADI)紧致差分格式.在时间方向上用二阶向后微分公式离散一阶时间导数,积分项用二阶卷积求积公式近似,在空间方向上用四阶精度的紧致差分离散二阶空间导数得到全离散紧致差分格式.基于与卷积求积相对应的实二次型的非负性,利用能量方法研究了差分格式的稳定性和收敛性,理论结果表明紧致差分格式的收敛阶为O(k~(a+1)+h_1~4+h_2~4),其中k为时间步长,h_1和h_2分别是空间x和y方向的步长.最后,数值算例验证了理论分析的正确性.  相似文献   

10.
构造了拟线性抛物型方程组初边值问题的一类具有界面外推的并行本性差分格式. 为给出子区域间界面上的值或者与界面相邻点处的值,给出了两类时间外推的方式, 得到了二阶精度无条件稳定的并行差分格式. 并且不作启示性假定,证明了所构造的并行差分格式的离散向量解的存在性和 唯一性. 而且在格式的离散向量解对原始问题的已知离散数据连续依赖的意义下, 证明了并行差分格式的解按离散W(2,1)2(QΔ)范数是无条件稳定的.最后证明了具有界面外推的并行本性差分格式的离散向量解收敛到原始拟线性抛物问题的唯一广义解. 给出了数值例子,数值结果表明所构造的格式是无条件稳定的, 具有二阶精度,且具有高度并行性.  相似文献   

11.
腾飞  孙萍  罗振东 《计算数学》2011,33(4):373-386
本文将特征正交分解(Proper Orthogonal Decomposition,简记为POD)方法应用于抛物型方程通常时间二阶中心差的时间二阶精度有限元格式(简称为通常格式),简化其为一个自由度极少但具有时间二阶精度的有限元格式,并给出简化的时间二阶中心差的时间二阶精度有限元格式(简称为简化格式)解的误差分析.数值...  相似文献   

12.
In this paper, a fast second‐order accurate difference scheme is proposed for solving the space–time fractional equation. The temporal Caputo derivative is approximated by ?L2 ‐1σ formula which employs the sum‐of‐exponential approximation to the kernel function appeared in Caputo derivative. The second‐order linear spline approximation is applied to the spatial Riemann–Liouville derivative. At each time step, a fast algorithm, the preconditioned conjugate gradient normal residual method with a circulant preconditioner (PCGNR), is used to solve the resulting system that reduces the storage and computational cost significantly. The unique solvability and unconditional convergence of the difference scheme are shown by the discrete energy method. Numerical examples are given to verify numerical accuracy and efficiency of the difference schemes.  相似文献   

13.
A second‐order finite difference scheme for mixed boundary value problems is presented. This scheme does not require the tangential derivative of the Neumann datum. It is designed for applications in which the Neumann condition is available only in discretized form. The second‐order convergence of the scheme is proven and the theory is validated by numerical examples. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 400–420, 2007  相似文献   

14.
A simple method is presented which determines the numerical stability or instability in the computation of any solution of a three-term homogeneous linear difference equation of order m in terms of the size of a single parameter. The method is illustrated by application to a second order and to a third order difference equation. Excellent agreement with predictions is reported.  相似文献   

15.
In the nonlinear regression model we consider the optimal design problem with a second order design D-criterion. Our purpose is to present a general approach to this problem, which includes the asymptotic second order bias and variance criterion of the least squares estimator and criteria using the volume of confidence regions based on different statistics. Under assumptions of regularity for these statistics a second order approximation of the volume of these regions is derived which is proposed as a quadratic optimality criterion. These criteria include volumes of confidence regions based on the u n - representable statistics. An important difference between the criteria presented in this paper and the second order criteria commonly employed in the recent literature is that the former criteria are independent of the vector of residuals. Moreover, a refined version of the commonly applied criteria is obtained, which also includes effects of nonlinearity caused by third derivatives of the response function.  相似文献   

16.
A simple second‐order finite difference treatment of polar coordinate singularity for Poisson equation on a disk is presented. By manipulating the grid point locations, we can successfully avoid finding numerical boundary condition at the origin so that the resulting matrix is simpler than traditional schemes. The treatments for Dirichlet and Neumann boundary problems are slightly different by adjusting the radial mesh width. Furthermore, the present discretization can be applied with slight modifications to Helmholtz‐type equations. The numerical evidence shows that the second‐order accuracy can also be preserved. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 199–203, 2001  相似文献   

17.
A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Neumann boundary value problem of a nonlinear parabolic system. It is proved that the difference scheme is uniquely solvable and second‐order convergent in L‐norm. A numerical example is given. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 230–247, 2004  相似文献   

18.
A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Dirichlet boundary value problem of the nonlinear parabolic systems. It is proved that the difference scheme is uniquely solvable and second order convergent in Lnorm. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 638–652, 2003  相似文献   

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