对流扩散方程的三次样条差分格式

Cubic spline difference scheme of convection-diffusion equation

提出了两种新的求解对流扩散方程的三次样条差分格式。首先利用变换将对流扩散方程变为扩散方程,然后分别结合二阶和四阶精度的三次样条公式获得两个无条件稳定的差分格式,其局部截断误差分别为O(t2+h2)和O(t2+h4)。数值实验表明,文中方法优于以往的三次样条方法。

Two new methods are presented for solving convection-diffusion equation.Firstly,a functional transformation is introduced and the convection-diffusion equation is transferred to the diffusion equation.Then,by utilizing the cubic spline difference formula of two and four order accuracy,two unconditionally stable schemes are obtained.The local truncation error of the new methods are O（t^2＋h^2）and O（t^2＋h^4）.Numerical experiment shows that the new methods are better than some other cubic spline methods.