对流占优扩散方程的改进特征差分算法

A Kind of Modified Characteristic-difference Schemes for Convection-diffusion Equations

将特征线方法和有限差分方法相结合,给出了一种求解对流占优扩散方程数值解的新的隐式特征差分格式,并研究了新算法的收敛性。新算法的优点是适应性强,特别适用于变系数方程,数值试验的结果表明在消除数值震荡方面更有效。

A new kind of characteristic-difference schemes for convection-diffusion equations is constructed by characteristic method and linear interpolation method. The convergence of the characteristic-difference scheme is proved. Its advantage is very adaptable, to obtain the solution to equations with variable coefficients. The numerical experiment shows the scheme is more efficient to reduce the oscillations.