对流扩散方程的一种高精度特征差分格式

A Class of High Accuracy Characteristic Difference Method for Convection-Diffusion Equations

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特征差分格式.通过Fourier方法讨论了文中格式的稳定性.数值结果表明,本文的格式明显优于基于线性插值的特征差分格式.

A new kind of characteristic-difference scheme is proposed for solving convection-diffusion (equations) with the linear interpolation method.The method is based on the cubic-spline difference formulae of fourth-order accuracy for second order derivatives developed by the other authors.The stability of the characteristic-difference scheme is studied.Numerical results show that our method is better than that of the ordinary characteristic-difference scheme with linear interpolation method.