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1.
本文构造了一类求解非线性时滞双曲型偏微分方程的紧致差分格式,获得了该差分格式的唯一可解性,收敛性和无条件稳定性,收敛阶为O(τ2+h4),并进一步对时间方向进行Richardson外推,使得收敛阶达到了O(τ4+h4).数值实验表明了算法的精度和有效性. 相似文献
2.
时间分数阶四阶扩散方程是一类重要的发展型偏微分方程,其数值解的研究有重要的科学意义和工程实际价值.本文针对时间分数阶四阶扩散方程,研究一类显-隐(E-I)差分格式和隐-显(I-E)差分格式解法,该方法基于经典隐式和经典显式格式相结合构造而成,分析E-I和I-E两种差分格式解的存在唯一性、稳定性和收敛性.理论分析和数值试验结果证实本文E-I差分格式和I-E差分格式无条件稳定,具有空间2阶精度,时间2-α阶精度.在计算精度一致的要求下,E-I和I-E差分格式较经典隐式差分格式具有省时性,其计算时间相比古典隐格式减少约70%,研究表明本文格式求解时间分数阶四阶扩散方程是有效的. 相似文献
3.
本文结合非等距网格高精度紧致差分格式的优越性与多重网格方法的快速收敛性,求解二维对流扩散方程。研究结果表明,对于处理物理量在不同的空间方向呈现不同的性态特征或不同变化规律的物理问题时,用非等距网格离散的四阶紧致格式的多重网格算法和二阶中心差分格式的多重网格算法都比等距网格离散得高效。同时,在非等距网格下下,部分半粗化多重网格算法比完全粗化多重网格算法具有更高的计算效率。针对不同的松弛算子对误差残量的磨光效果比较研究表明,线松弛算子是最高效的。而且,非等距网格离散的高精度紧致格式的多重网格算法对于对流扩散问题中大网格雷诺数情形也是收敛的。 相似文献
4.
一维非定常对流扩散方程的高阶组合紧致迎风格式 总被引:1,自引:0,他引:1
赵秉新 《数值计算与计算机应用》2012,33(2):138-148
通过将对流项采用四五阶组合迎风紧致格式离散,扩散项采用四阶对称紧致格式离散之后,对得到的半离散格式在时间方向采用四阶龙格库塔方法求解,从而得到了一种求解非定常对流扩散方程问题的高精度组合紧致有限差分格式,其收敛阶为O(h~4+τ~4).经Fourier精度分析和数值验证,证实了格式的良好性能.三个数值算例包括线性常系数问题,矩形波问题和非线性问题,数值结果表明:该格式具有很高的分辨率,且适用于对高雷诺数问题的数值模拟. 相似文献
5.
Burgers方程为Navier-Stokes方程组的简化形式,在计算数学和计算流体力学领域中有着广泛应用.本文设计了粘性Burgers方程的高阶精度半隐式加权紧致非线性格式(WCNS),并给出了稳定性分析.方程对流项和粘性项分别采用五阶精度WCNS格式和四阶中心差分格式计算.半离散系统采用三阶精度IMEX Runge... 相似文献
6.
通过将原方程变换为对流扩散方程,将所得方程的对流项采用四阶组合紧致迎风格式离散,扩散项采用四阶对称紧致格式离散之后,对得到的空间半离散格式采用四阶龙格库塔方法进行时间推进,得到了一种求解非定常对流扩散反应问题的高精度方法,其收敛阶为O(h4+τ4).经数值实验并与文献结果进行对比,表明该格式适用于对流占优问题的数值模拟,验证了格式的良好性能. 相似文献
7.
《计算机研究与发展》1963,(2)
W.Urich描述了一个差分方法,它用于近似求解含有m个方程、m个未知函数及n+1个自变量的一阶拟线性偏微分方程组的初值问题。这方法是根据这样一种事实:在每一个方程中,同一个函数的偏导数定义了一个方向导 相似文献
8.
9.
用联合紧致差分格式(CCD)离散Helmholtz方程,具有6阶精度.然而对于得到的线性方程组,我们仍需一种高效求解方法.本文针对二维的Helmholtz方程CCD离散所得的线性方程组给出高效的数值方法.数值例子表明所提出的方法是有效的. 相似文献
10.
针对广义Maxwell粘弹性流体分数阶微分方程,建立了一种隐式差分格式,给出了数值解的求解公式,证明了隐式差分格式稳定性与收敛性。 相似文献
11.
L. K. Bieniasz 《Computing》2007,81(1):77-89
Summary The extended Numerov scheme of Chawla, adopted for nonuniform grids, is a useful compact finite-difference discretisation,
suitable for the numerical solution of boundary value problems in singularly perturbed second order non-linear ordinary differential
equations. A new set of three-point compact approximations to first and second derivatives, related to the Chawla scheme and
valid for nonuniform grids, is developed in the present work. The approximations economically re-use intermediate quantities
occurring in the Chawla scheme. The theoretical orders of accuracy are equal four for the central and one-sided first derivative
approximations obtained, whereas the central second derivative formula is either fourth, third, or second order accurate,
depending on the grid ratio. The approximations can be used for accurate a posteriori derivative evaluations. A Hermitian
interpolation polynomial, consistent with the derivative approximations, is also derived. The values of the polynomial can
be used, among other things, for guiding adaptive grid refinement. Accuracy orders of the new derivative approximations, and
of the interpolating polynomial, are verified by computational experiments.
相似文献
12.
A new high spectral accuracy compact difference scheme is proposed here. This has been obtained by constrained optimization of error in spectral space for discretizing first derivative for problems with non-periodic boundary condition. This produces a scheme with the highest spectral accuracy among all known compact schemes, although this is formally only second-order accurate. Solution of Navier-Stokes equation for incompressible flows are reported here using this scheme to solve two fluid flow instability problems that are difficult to solve using explicit schemes. The first problem investigates the effect of wind-shear past bluff-body and the second problem involves predicting a vortex-induced instability. 相似文献
13.
This paper provides an implicit central compact scheme for the numerical solution of incompressible Navier–Stokes equations. The solution procedure is based on the artificial compressibility method that transforms the governing equations into a hyperbolic-parabolic form. A fourth-order central compact scheme with a sixth-order numerical filtering is used for the discretization of convective terms and fourth-order central compact scheme for the viscous terms. Dual-time stepping approach is applied to time discretization with backward Euler difference scheme to the pseudo-time derivative, and three point second-order backward difference scheme to the physical time derivative. An approximate factorization-based alternating direction implicit scheme is used to solve the resulting block tridiagonal system of equations. The accuracy and efficiency of the proposed numerical method is verified by simulating several two-dimensional steady and unsteady benchmark problems. 相似文献
14.
The problem of finding the solution of partial differential equations with source control parameter has appeared increasingly in physical phenomena, for example, in the study of heat conduction process, thermo-elasticity, chemical diffusion and control theory. In this paper we present a high order scheme for determining unknown control parameter and unknown solution of parabolic inverse problem with both integral overspecialization and overspecialization at a point in the spatial domain. In these equations, we first approximate the spatial derivative with a fourth order compact scheme and reduce the problem to a system of ordinary differential equations (ODEs). Then we apply a fourth order boundary value method for the solution of resulting system of ODEs. So the proposed method has fourth order accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. Several numerical examples and also some comparisons with other methods in the literature will be investigated to confirm the efficiency of the new procedure. 相似文献
15.
Difference schemes that are compact in space, i.e., schemes constructed on a two- or three-point stencil in each spatial direction, are more efficient and convenient for boundary condition formulation than other high-order accurate schemes. Originally, these schemes were developed primarily to obtain smooth solutions. In the last two decades, compact schemes have been actively used to compute gas dynamic flows with shock waves. However, when a numerical solution with guaranteed accuracy is desired, the actual properties of difference schemes have to be known in the calculation of solutions with discontinuities. For some widely used compact schemes, this issue has not yet been well studied. The properties of compact schemes constructed by the method of lines are examined in this paper. An initial-boundary value problem for the linear heat equation with discontinuous initial data is used as a test problem. In the method of lines, the spatial derivative in the heat equation is approximated on a two-point stencil according to a fourth-order accurate compact differentiation formula. The resulting evolution system of ordinary differential equations is solved using various implicit one-step two- and three-stage schemes of the second and third order of accuracy. The relation between the properties of the stability function of a scheme and the spatial monotonicity of the numerical solution is analyzed. In computations over long time intervals, the compact schemes are shown to be superior to traditional schemes based on the second-order accurate three-point approximation of the spatial derivative. 相似文献
16.
《国际计算机数学杂志》2012,89(6):747-763
A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational method is suggested in this paper. This method combines an exponentially fitted finite difference scheme and a classical finite difference scheme. The proposed method is distinguished by the fact that, first we divide the domain of definition of the differential equation into three subintervals called inner and outer regions. Then we solve the boundary value problem over these regions as two point boundary value problems. The terminal boundary conditions of the inner regions are obtained using zero order asymptotic expansion approximation of the solution of the problem. The present method can be extended to system of two equations, of which, one is a first order ODE and the other is a singularly perturbed second order ODE. Examples are presented to illustrate the method. 相似文献
17.
In the event of an accidental leakage of high level radioactive waste buried deep in repositories surrounded by rock, the build up of the concentration of the radioactive species within the rock needs to be assessed. Towards this, we follow the model of Chen and Li and provide a numerical code to solve the relevant partial differential equations using a compact finite difference scheme. 相似文献
18.
This paper outlines a reliable strategy to use the homotopy perturbation method based on Jumarie’s derivative for solving fractional differential equations. In this framework, compact structures of fourth-order fractional diffusion-wave equations are considered as prototype examples. Moreover, convergence of the proposed approach for these types of equations is investigated. Results show that the response expressions are Mittag-Leffler stable. 相似文献
19.
Xin-rong Cong 《国际计算机数学杂志》2018,95(2):316-328
The high-order accurate compact finite difference scheme which belongs to the finite difference methods is constructed to solve the system of partial differential equations with random noise. The error analysis and stability analysis are given and then the numerical simulation is executed. The simulation results verify the theoretical analysis results and have the faster computation speed and higher accuracy. 相似文献
20.
《国际计算机数学杂志》2012,89(16):3553-3564
In this paper, a numerical method is developed to solve an N-carrier system with Neumann boundary conditions. First, we apply the compact finite difference scheme of fourth order for discretizing spatial derivatives at the interior points. Then, we develop a new combined compact finite difference scheme for the boundary, which also has fourth-order accuracy. Lastly, by using a Padé approximation method for the resulting linear system of ordinary differential equations, a new compact finite difference scheme is obtained. The present scheme has second-order accuracy in time direction and fourth-order accuracy in space direction. It is shown that the scheme is unconditionally stable. The present scheme is tested by two numerical examples, which show that the convergence rate with respect to the spatial variable from the new scheme is higher and the solution is much more accurate when compared with those obtained by using other previous methods. 相似文献