一维变系数对流扩散方程的一个紧致差分格式

摘要

对一维变系数的对流扩散方程提出了一个紧致差分格式，从而将格式的收敛阶提高为 O（τ2＋ h4），通过Fou-rier级数的方法和L ax等价性定理证明了差分格式的稳定性和收敛性，数值实验结果很好地验证了理论的正确性。%In this paper ,a compact finite difference scheme is presented for 1D convection-diffusion equations with variable coefficients .The convergence order is O(τ2 + h4 ) .The stability and convergence are proved by Fourier method and Lax equivalence theorem .The numerical results have been carried out to confirm the correctness of the theory .