三维热传导方程的一族两层显式格式

提出了一族三维热传导方程的两层显式差分格式,当截断误差阶为O(Δt+(Δx)2)时,稳定性条件为网格比r=Δt/(Δx)2=Δt/(Δy)2=Δt/(Δz)2≤1/2,优于其他显式差分格式。而当截断误差阶为O((Δt)2+(Δx)4)时,稳定性条件为r≤1/6,包含了已有的结果。     

解高维热传导方程的一族高精度的显式差分格式

本文构造出针对三维和四维热传导方程的一族高精度的显格式,其截断误差阶达到Ｏ（τ＾２＋ｈ＾４）,并给出了稳定性条件,通过数值实例,验证了此方法较周顺兴（１９８０年）的结果提高二位以上有效数字。     

解三维热传导方程的一族对称含参数高精度的显式差分格式

对求解三维热传导方程利用待定参数法构造出一族对称的含参数的，截断误差为Ｏ（Δｔ＾１＋Δｘ＾４＋Δｙ＾４＋Δｚ＾４）的便于计算的三层显格式，并讨论了其条件稳定性。     

解三维热传导方程的一种高精度的显格式

对解三维热传导方程利用待定参数方法构造出一种精度O(Δt2+Δx4+Δy4+Δz4)的高精度易于计算的显式差分格式,并给出了其稳定性,通过数值例子可见其精度较其它方法提高2～3位有效数字。     

二维抛物型方程的一族高精度分支稳定显格式

1 引言 在渗流、扩散、热传导等领域中经常会遇到求解二维抛物型方程的初边值问题 {(6)u/(6)=a((6)2u/(6)x2+(6)2u/(6)y2), 0＜x,y＜L,t＞0,a＞0u(x, y, 0) =φ(x, y), 0 ≤ x, y ≤ L (1)u(0,y,t) =f1(y,t),u(L,y,t) =f2...     

解抛物型方程的分支稳定的高精度显式差分格式

用待定参数法构造了解一维抛物型方程的分支稳定的高精度显式差分格式,截断误差为O（△t^4△x^4),稳定性条件为r=a△t/△x^2＜1/2。     

解高维热传导方程的一个高精度ADI格式

构造了一个解四维热传导方程的一个高精度ADI格式,格式绝对稳定,截断误差阶达到O(△t~2 △x~4).可用追赶法求解.     

二维热传导方程的三层显式差分格式

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。     

三维抛物型方程的一族高精度分支稳定显格式

构造了一族解三维抛物型方程的高精度显格式,其稳定性条件为r=Δt/Δx2=Δt/Δy2=Δt/Δz2<1/2,截断误差为O(Δt2+Δx4).     

高维热传导方程的高精度分支显格式

A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed.The stability condition is r = △t/△x2 = △t/△y2 = △t/△]z2 = △t/△w2＜3/8,and the truncation error is O(△t2 △x4).     

解三维抛物型方程的一个ADI格式

构造了一个解三维抛物型方程的高精度ADI格式,格式绝对稳定,截断误差为O（△t^2＋△x^4）;然后应用Richerdson外推法,外推一次得到了具有O（△t^3＋△x^6）阶精度的近似解.     

三维抛物型方程的一个高精度恒稳定的PC格式

对三维抛物型方程,构造了一个高精度恒稳定的PC格式,格式的截断误差阶达到O（△t^2＋△x^4）,通过数值实例验证了所得格式较现有的同类格式的精度提高了二位以上有效数字;然后将Richardson外推法应用于本文格式,得到了具有O（△t^3＋△x^6）阶精度的近似解,并将所得格式推广到了四维情形．     

A class of difference scheme for solving telegraph equation by new non-polynomial spline methods

In this paper, by using a new non-polynomial parameters cubic spline in space direction and compact finite difference in time direction, we get a class of new high accuracy scheme of O(τ⁴ + h²) and O(τ⁴ + h⁴) for solving telegraph equation if we suitably choose the cubic spline parameters. Meanwhile, stability condition of the difference scheme has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.     

A three-time-level explicit difference scheme of the second order of accuracy for parabolic equations

The difference schemes of Richardson [1] and of Crank-Nicolson [2] are schemes providing second-order approximation. Richardson's three-time-level difference scheme is explicit but unstable and the Crank-Nicolson two-time-level difference scheme is stable but implicit. Explicit numerical methods are preferable for parallel computations. In this paper, an explicit three-time-level difference scheme of the second order of accuracy is constructed for parabolic equations by combining Richardson's scheme with that of Crank-Nicolson. Restrictions on the time step required for the stability of the proposed difference scheme are similar to those that are necessary for the stability of the two-time-level explicit difference scheme, but the former are slightly less onerous.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 751–759, November, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00489 and by the International Science Foundation under grants No. N8Q300 and No. JBR100.     

A compact alternate direct implicit difference method for solving parabolic equation of multi-dimension

A compact alternate direct implicit difference method for multi-dimensional parabolic equation is studied in this paper. Firstly, a compact difference scheme is derived by using the operator method and the expression of the truncation error is given. Secondly     

A finite difference scheme for solving the heat transport equation at the microscale

Heat transport at the microscale is of vital importance in microtechnology applications. In this study, we develop a finite difference scheme of the Crank‐Nicholson type by introducing an intermediate function for the heat transport equation at the microscale. It is shown by the discrete energy method that the scheme is unconditionally stable. Numerical results show that the solution is accurate. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 697–708, 1999     

An economical difference scheme for heat transport equation at the microscale

Heat transport at the microscale is of vital importance in microtechnology applications. In this article, we proposed a new ADI difference scheme of the Crank‐Nicholson type for heat transport equation at the microscale. It is shown that the scheme is second order accurate in time and in space in the H¹ norm. Numerical result implies that the theoretical analysis is correct and the scheme is effective. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Alternating group explicit method for the diffusion equation

A new alternating group explicit method is presented for the finite difference solution of the diffusion equation. The new method uses stable asymmetric approximations to the partial differential equation which, when coupled in groups of two adjacent points on the grid, result in implicit equations which can be easily converted to explicit form and which offer many advantages. By judicious alternation of this strategy on the grid points of the domain an algorithm which possesses unconditional stability is obtained. This approach also results in more accurate solutions because of truncation error cancellations. The stability, consistency, convergence and truncation error of the new method are briefly discussed and the results of numerical experiments presented.