Stability And A Posteriori Estimate For The Variable Step-size BDF2 Method For Parabolic Equation With Delay

Parabolic equations with delay has been widely used 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.The paper mainly deals with the following linear delay parabolic equation u'(t)+ Au(t)+ Bu(?(t))= f(t),t ?[0,T],u(t)=? t?[t-1,0].We study a posteriori error estimates of the variable step-size BDF2 method for it.The conclusions are as follows:1.The stability of variable step-size BDF2 method for linear delay parabolic equations is proved.2.A posteriori error estimates of variable step-size BDF2 method(including two reconstructions)for linear delay parabolic equations are given.