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(τ2+τh2+h4),即当τ=O(h2)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 one-dimensional 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 when τ=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.
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