摘要
根据已发展的二阶微商三次样条四阶逼近公式,提出了基于线性插值的求解对流扩散方程的特征差分格式。通过 Fourier 方法讨论了该格式的稳定性。数值结果表明,本文对对流扩散方程给出的特征差分格式明显优于一般的基于线性插值的特征差分格式。
利用第二类 Saul’yev 非对称格式给出了对流扩散方程的一类交替分组显格式。该方法具有并行本性,并且绝对稳定。数值结果表明,本文对对流扩散方程给出的 AGE 算法明显优于 Evans 和 Abdullah[15]所提出的交替分组显格式,因此本文方法是一种有效算法。
将特征线法和有限差分法相结合,借助于斜线性插值,分别给出了求解线性和非线性对流占优扩散方程的一种新的特征差分格式,并研究了算法的收敛性。该算法的优点是特别适用于求解变系数的对流占优扩散方程,能更有效地消除数值振荡现象。
A new kind of characteristic-difference scheme is proposed for solving convecti -on diffusion equations with the linear interpolation method.The method is based on the cubic-spline difference formular of fourth-order accuracy for second order deriva -tives developed byTian Zhenfu.The stability of the characteristic difference scheme is studied.The results prove that our method is better than the ordinary characteristic difference scheme with the linear interpolation method.
Based on the Saul’yev asymmetric schemes, a new alternating group explicit (AGE)method for solving convection-diffusion equation is derived in this paper. The method has the obvious property of parallelism,and is unconditionally stable. Numer -ical example is given which illustrated that the present method is in preference to Evans and Abdullah’AGE method for solving the convection-diffusion equation in [15].
A new kind of characteristic-difference scheme for convection-dominated diffus -ion equations is constructed by combining characteristic method with the finite -difference method and with the skew linear interpolation method. The convergence of the characteristic-difference scheme is studied. The advantage of this scheme is very adaptable to obtain the solution of the equations with variable coefficient and can eliminate the numerical oscillations more efficiently.
引文
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