延迟抛物型方程二阶BDF方法的稳定性和后验误差估计

Stability and Posteriori Estimates for the Variable Step--size BDF2 Method to Parabolic Equations with Delay

延迟微分方程在科学与工程等多个领域中有着广泛应用.本文考虑延迟抛物型方程的时间逼近.首先证明延迟抛物型方程二阶变步长BDF方法的稳定性,进而通过重构获得更高阶的数值逼近,由此获得二阶变步长BDF方法的后验误差估计.

Parabolic equations with delay has been widely appeared in scientific and engineering fields.In this paper we consider the time approximation of parabolic equations with delay.Firstly,we prove the stability of variable step--size BDF2 method for parabolic equations with delay.Then,we derive a higher order numerical approximation by reconstruction.Finally,we obtain a posteriori estimates of variable step--size BDF2 method for the equations.