抛物方程的一类并行差分格式

A Parallel Difference Scheme for Parabolic Equation

讨论一类数值求解热传导方程具并行本性的差分方法.在此法中,通过引进内界点,将求解区域分裂成若干子区域.在子区域间内界点上的值可显式求解,一旦这些值被计算出来,各子区域上完全可并行求解.本文得到了稳定性条件和最大模误差估计,表明此格式稳定性强,并且有较高的收敛阶.

The present paper deals with the finite difference scheme with intrinsic parallelism for numerically solving the heat equation. In this procedure, the domain over which the problem is defined is divided into subdomains by introducing interface points. The interface values between subdomains are found by explicit formulas, once these values have been calculated, subdomain problems can be solved in parallel. The stability conditions and maximum norm error estimates for these procedures have been derived, which demonstrate that our schemes have satisfactory stability and higher convergence order.