The Long-term Convergence And Error Estimation Of The Differential Solution Of The Reaction-diffusion Equation

In this paper,a finite difference scheme for the initial-boundary value problem of a reaction-diffusion equation is established.The whole paper is described in four chapters.The first chapter is the introduction part.First,the background and development of the nonlinear dynamic system are introduced.Secondly,the formation and development of reaction-diffusion equation are introduced as well as the operation process of the finite difference method commonly used to solve this kind of problem are also introduced.Then,the research status and achievements at home and abroad are introduced and the purpose and significance of this research are finally drawn.In the second chapter,we give some preliminary knowledge,mainly some symbols and hypotheses related to this paper.Then we use the finite difference method to discretize the problem and establish the backward Euler difference scheme.At the same time,we give some lemmas needed in this paper and a main theorem to be studied in this paper.In Chapter 3 and Chapter 4,the long-time properties of the solutions of the finite difference schemes are studied,and the existence and uniqueness of the difference solutions are proved in detail.Finally,we fully discuss the convergence of the difference solutions in bounded time [0,T ] and unbounded time [T,+?],and give the error estimates between the difference solutions and the exact solutions.