求解一维对流扩散方程的一种三层有限差分格式

Three-level Finite Difference Technique for the One-dimensional Advection-diffusion Equation

通过指数变换将方程变形,消去方程中的"对流项",再利用反指数变换和待定系数法,构造了求解一维对流扩散方程的一种三层差分格式。采用Von Neumann方法分析了差分格式的稳定性,得到了格式稳定的充分必要条件。

Various numerical techniques will be developed and compared for solving one - dimensional advection - diffusion equation with constant coefficient. These techniques are based on the exponent transform. It allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. The new method is more accurate and is more efficient than the conventional technique. The scheme is free of numerical diffusion. The resuits of a numerical experiment are presented, and the accuracy is dicussed and compared.