A Posteriori Error Estimates Of The Crank-Nicolson Method For Parabolic Equation With Delay

Delay parabolic differential equations axe widely used in many fields,such as economics,physical chemistry,ecology,medicine,nuclear engineering.Therefore,it is very important to research the numerical solution.There are many papers devoted to the stability analysis and a priori error estimates for the delay parabolic equation.But there is no result of a posteriori error estimate for the numerical solution of the delay parabolic equation.In this paper,we consider the a posterior error estimation of the Crank-Nicolson method for delay parabolic equations for the first time.Because of the weak discontinu-ity of the true solution to delay parabolic equations,which will bring many difficulties to the research of error estimation,it is important to realize step control and adap-tive calculation in the actual calculation,the study of the algorithm a posteriori error estimation is particularly important.The paper mainly deals with the following linear delay parabolic equationWe study a posteriori error estimates of the Crank-Nicolson method for them.The conclusions are as follows:1.The stability of Crank-Nicolson method for linear delay parabolic equations is proved.2.A posteriori error estimates of Crank-Nicolson method and Crank-Nicolson-Galerkin method for linear delay parabolic equations are given.Finally,the numerical experiments conform our conclusions.