共查询到20条相似文献,搜索用时 15 毫秒
1.
一族新的高精度显式差分格式 总被引:1,自引:1,他引:0
对求解三维势物型偏微分方程,利用待定参数法构造出一族新的高精度的三层显式差分格式,其精度为O(△t^3+△x^4+△y^4+△z^4),并论证了其稳定性,通过数值实例可见其精度较文「1」提高2位有效数字。 相似文献
2.
马明书 《应用数学和力学(英文版)》1996,17(11):1075-1079
A-HIGH-ORDERACCURACYEXPLICITDIFFERENCESCHEMEFORSOLVINGTHEEQUATIONOFTWO-DIMENSIONALPARABOLICTYPEMaMingshu(马明书)(ReceivedJune2,1... 相似文献
3.
Ma Mingshu 《应用数学和力学(英文版)》1998,19(5):497-501
In this paper, a new three-level explicit difference scheme with high-orderaccuracy is proposed for solving three-dimensional parabolic equations. The stabilitycondition is r=△t/△x2 =△t/△y2=△t/△z2≤1/4, and the trumcation error is O(△t2+△x4). 相似文献
4.
曾文平 《应用数学和力学(英文版)》2000,21(9):1071-1078
IntroductionThispaperdealswiththeinitial_boundaryvalueproblemofthree_dimensionalheatconductionequationintheregionD :0≤x,y ,z≤L ,0 ≤t≤T u t= 2 u x2 2 u y2 2 u z2 ,u|x=0 =f1(y,z,t) , u|x=L =f2 (y ,z,t) ,u|y=0 =g1(z,x,t) , u|y=L =g2 (z,x,t) ,u|z=0 =h1(x ,y ,t) , u|z=L =h2 (x ,y ,t) ,u|t=0 =φ(x ,y,z) .(1 )(2 )… 相似文献
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IntroductionWeoftenmeettheproblemofsolvingequationofparabolictypeinmanyfieldssuchasseepage ,diffusion ,heatconductionandsoon .Inthecaseof3_dimension ,themodelisaninitialandboundaryvalueproblemasfollows: u t = 2 u x2 2 u y2 2 u z2 (0 <x,y,z<1 ;t>0 ) ,u(x ,y,z,0 ) =φ(x ,y ,z)… 相似文献
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对一类时滞抛物型方程初边值问题,提出了关于空间步长是四阶精度的高精度无条件稳定的精细积分法.数值算例表明,本文提出的精细积分法具有很高的精度,因而是一种有效的数值方法. 相似文献
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刘继军 《应用数学和力学(英文版)》2003,24(5):605-613
A 3-layered explicit difference scheme for the numerical solution of 2-D heat equation is proposed. Firstly, a general symmetric
difference scheme is constructed and its optimal error is obtained. Then two kinds of condition for choosing the parameters
for optimal error and stable difference scheme are given. Finally, some numerical results are presented to show the advantage
of the schemes
Foundation items: the Science Foundation of Chinese Postdoctoral (2002031224); the Science Foundations of Southeast University (9209011148,
3007011043)
Biography: Liu Ji-jun (1965-) 相似文献
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孙其仁 《应用数学和力学(英文版)》1991,12(12):1209-1215
This paper proposes a new method to improve the stability condition of differencescheme of a parabolic equation.Necessary and sufficient conditions of the stability of thisnew method are given and proved.Some numerical examples show that this method hassome calculation advantages. 相似文献
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The explicit compact difference scheme,proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al.,published in Applied Mathematics and Mechanics (English Edition),2007,28(7),943-953,has the same performance as the conventional finite difference schemes.It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless,we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations,especially for higher accurate schemes. 相似文献
10.
黎益 《应用数学和力学(英文版)》1993,14(3):235-239
A class of three-level explicit difference schemes for the dispersive equationu_1=au_(xxx)are established These schemes have higher stability and involve four meshpoints at the middle level.Their local truncation errors are O(τ+h)and stabilityconditions are from|R|≤0.25 to|R|≤10,where|R|=|a|τ/h~3,which is muchbetter than|R|≤0.25. 相似文献
11.
The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics (English Edition), 2007, 28(7), 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes. 相似文献
12.
Eric Ngondiep 《国际流体数值方法杂志》2020,92(4):266-284
This work deals with the numerical solutions of two-dimensional viscous coupled Burgers' equations with appropriate initial and boundary conditions using a three-level explicit time-split MacCormack approach. In this technique, the differential operators split the two-dimensional problem into two pieces so that the two-step explicit MacCormack scheme can be easily applied to each subproblem. This reduces the computational cost of the algorithm. For low Reynolds numbers, the proposed method is second-order accurate in time and fourth-order convergent in space, whereas it is second-order convergent in both time and space for high Reynolds numbers problems. This observation shows the utility and efficiency of the considered method compared with a broad range of numerical schemes widely studied in the literature for solving the two-dimensional time-dependent nonlinear coupled Burgers' equations. A large set of numerical examples that confirm the theoretical results are presented and critically discussed. 相似文献
13.
Based on the successive iteration in the Taylor series expansion method,a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper.Numerical characteristics of the scheme are studied by the Fourier analysis. Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node,the proposed scheme is explicit and can achieve arbitrary order of accuracy in space.Application examples for the convection- diffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given.It is found that the proposed compact scheme is not only simple to implement and economical to use,but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems. 相似文献
14.
Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems. 相似文献
15.
Galerkin domain decomposition procedures for parabolic equations with three cases of boundary conditions on rectangular domain are discussed. These procedures are non‐iterative and non‐overlapping ones. They rely on implicit Galerkin method in the sub‐domains and integral mean method on the inter‐domain boundaries to present explicit flux calculation. Thus, the parallelism can be achieved by the use of these procedures. Two kinds of approximating schemes are presented. Because of the explicit nature of the flux calculation, a less severe time‐step constraint is derived to preserve stability. To bound L2‐norm error estimates, new elliptic projections are established and analyzed. Numerical experiments are provided to confirm theoretical results. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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色散方程的高稳定性两层四点显格式的单点精细积分法 总被引:1,自引:0,他引:1
基于单点精细积分的思想,对色散方程Ut=aUxxx构造了一类高稳定性的两层四点显式差分格式,其局部截断误差为O(τ+h)稳定性条件为│R│=│aτ/h^3│≤f(β),对任意正实数β为单调递增函数,它们不仅显著地改善了同类格式的稳定性条件│R│≤0.25而且也优于众多三层多点(5点或5点以上)显格式的稳定性条件。 相似文献
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In this paper, using nonumiform mesh and exponentially fitted difference method,a uniformly convergent difference scheme .for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter ε is given, and error estimate and numerical result are also given. 相似文献
20.
Let A cud B satisfy the Structural conditions (2), the local Hölder continuityinterior to Q=G×(0, T) is proved for the generalized solutions of quasilinearparabolic equations as follows: u2 - divA(x, t,u,∇u) + B(x, t, u, ∇u)=0 相似文献