一维非定常对流扩散反应方程的高精度紧致差分格式

High order compact difference scheme for the one-dimensional unsteady convection diffusion reaction equation

针对一维非定常对流扩散反应方程,首先推导了一种新的2层高精度紧致差分隐格式,其截断误差为O(τ~2+τh^2+h^4),即当τ=O(h^2)时,格式空间具有四阶精度;然后采用Fourier分析方法分析了格式的稳定性;最后通过数值算例验证了本文格式的精确性和可靠性.

A two-level high order compact finite difference implicit scheme is proposed to solve the onedimensional unsteady convection diffusion reaction equation.The local truncation error of the scheme is O（τ2＋τh2＋h4）,i.e.the scheme is the fourth order accuracy for space whenτ=O（h2）.Then,Fourier analysis method is used to prove the stability of the scheme.Finally,numerical experiments are conducted to verify the accuracy and the reliability of the present scheme.