Difference Method For Two Classes Of Delay Partial Differential Equations

This paper is concerned with difference method for two classes of delay partial differential equations. And we provide the theoretical analysis for them. Generally, it is very difficult to get the exact solutions of delay differential equations. Hence, it is very important to study the numerical methods both in theory and applied aspects.In recent decades, numerical study of delay differential equations has created an upsurge in the international community. Scholars have also put forward a number of numerical methods for solving delay differential equations, such as Runge-Kutta method, q method, Single-step configuration method. Numerical method has come to play an important role in many areas, such as Automatic control, Civil Engineering and Environmental Science.At the beginning of this article we introduce some basic knowledge and applications of difference method simply. Then the difference scheme of a class of differential partial equation which have a small constant delay have been constructed. We use the existing knowledge to analyze the scheme. Through some numerical examples we find that the numerical method showed in this paper is better than the classical methods. At last, we build a Crank-Nicolson difference scheme which is obtained by applying step-by-step methods to the resulting systems of delay partial differential equations. Sufficient and necessary conditions for the difference scheme to be stable are established. Numerical experiments have been implemented to confirm the stability of this numerical method.