对流占优扩散方程一种新的特征差分算法

A New Kind of Characteristic-Difference Algorithm for Convection-Diffusion Equations

将特征线法和有限差分法相结合,借助于双线性插值,给出了求解对流占优扩散方程数值解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震荡现象。

A new kind of characteristicdifference algorithm for convectiondiffusion equations is constructed by combining characteristic method with the finitedifference method and with the help of bilinear interpolation method. The convergence of the characteristicdifference algorithm is studied. The advantage of the algorithm is very adaptable to obtain the solution of the equations with variable coefficient and can eliminate the numerical oscillations more efficiently.