共查询到10条相似文献，搜索用时 31 毫秒
1.
Shimin Chai Yongkui Zou Chenguang Zhou Wenju Zhao 《Numerical Methods for Partial Differential Equations》2019,35(5):1745-1755
This paper is devoted to a newly developed weak Galerkin finite element method with the stabilization term for a linear fourth order parabolic equation, where weakly defined Laplacian operator over discontinuous functions is introduced. Priori estimates are developed and analyzed in L2 and an H2 type norm for both semi‐discrete and fully discrete schemes. And finally, numerical examples are provided to confirm the theoretical results. 相似文献
2.
In this article, we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two‐dimensional heat equation. We employ, respectively, second‐order and fourth‐order schemes for the spatial derivatives, and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is nonsingular. Numerical experiments carried out on serial computers show the unconditional stability of the proposed method and the high accuracy achieved by the fourth‐order scheme. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 54–63, 2001 相似文献
3.
This article is concerned with a high‐order difference scheme presented by Jain, Jain, and Mohanty for the nonlinear parabolic equation uxx = F(x, t, u, ut, ux) with Dirichlet boundary conditions. The solvability of the difference scheme is proved by Brower's fixed point theorem and the uniqueness of the difference solution is obtained by showing that the coefficient matrix is strictly column‐wise diagonal dominant. The boundedness and convergence of the difference scheme are obtained. The convergence order is 4 in space and 2 in time in L∞‐norm. A numerical example is provided to illustrate the validity of the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq , 2006 相似文献
4.
Kenneth Hvistendahl Karlsen;Nils Henrik Risebro 《Mathematical Modelling and Numerical Analysis》2001,35(2):239-269
We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a \"rough\"coefficient function k(x) . We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV , thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general Lp compactness criterion. https://doi.org/10.1051/m2an:2001114 相似文献
5.
对二维热传导方程构造了一个稳定的三层显式差分格式求其数值解,其背景源于高维热力学反问题迭代算法中对正问题小计算量算法的需求。首先建立一个含参数的一般差分格式去逼近微分方程,并得到了最优截断误差。然后导出了参数应满足的条件以保证差分格式的稳定性。最后给出了数值的例子并和其它算法进行比较,说明了格式在精度上的有效性和计算量上的优越性。 相似文献
6.
针对四阶抛物型方程周期初值问题,提出了一个两层隐式差分格式和一个三层隐式差分格式.它们的局部截断误差分别为O((Δt)2+(Δx)4)和O((Δt)2+(Δt)(Δx)2+(Δx)4),其中Δt,Δx分别为时间步长和空间步长.误差分析和数值实验均表明,本文构造的差分格式比经典的Crank-Nicolson格式和Saul’ev构造的差分格式精度更高.从精度及稳定性方面考虑,本文构造的格式也比文[5]的显式格式要好. 相似文献
7.
研究了一类带有周期边界条件的三维拟抛物粘性扩散方程有限差分解的长时间行为.证明了数值解的存在唯一性,离散系统全局吸引子的存在性,差分格式的长时间稳定性和收敛性.此外,我们给出了上半连续性. 相似文献
8.
研究了一类带有周期边界条件的三维拟抛物粘性扩散方程有限差分解的长时间行为.证明了数值解的存在唯一性,离散系统全局吸引子的存在性,差分格式的长时间稳定性和收敛性.此外,我们给出了上半连续性. 相似文献
9.
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. 相似文献
10.
抛物型方程非齐次边值问题的推广型LOD有限差分及有限元格式 总被引：5，自引：0，他引：5
1引言本文考虑区域Ω=[0,1]~d(d=2,3)上的非齐次抛物型方程第一边值问题(?)-C_1△u C_2u=f(x,t),x∈Ω,t∈(0,T],(1．1) u(x,0)=u_0(x),x∈Ω,(1．2) u(x,t)=(?)(x,t),x∈(?)Ω,t∈(0,T],(1．3)其中C_1,C_2为常数且C_1＞0,C_2≥0．对于以上问题,可以使用有限差分方法及有限元方法进行离散,并采用交替方向方法求解．交替方向方法能够将高维问题转化为一系列的一维问题进行计算,具有计算量少,计算稳定且易于并行实现等优点,在大规模科学计算中起着非常重要的作用,一直是计算数 相似文献