对流扩散方程的样条子域精细积分分步格式

The alternating segment method of spline sub-domain precise integration for convection-diffusion equation

基于子域精细积分的思想和分步技术,针对常系数对流扩散方程,提出了一类含参数α>0(α<<h)的样条子域精细积分分步格式,该方法是无条件稳定的,且非常适合于并行计算.数值试验结果表明,该方法是十分有效的,且可用于带有第2、3类边界条件问题的计算.

Based on sub-domain precise integration method and cubic spline function approximation, the alternating segment method of spline sub-domain precise integration containing parameter a 〉 0 for the first initial-boundary value problem of convection-diffusion equation was presented in this paper, which was unconditionally stable and had the advantages of parallel computing. The numerical example showed that the accuracy of the method was excellent, and the method could be conveniently used to solve the second and third initial-boundary value problems.