Reflect The Diffusion Equation With Constant Coefficients Of Four Dimensions Of Alternating Direction Difference Scheme

With the rapid development of science and technology,mathematical differential equation plays an irreplaceable role in theory and practical application,such as the development of oil,image analysis,aerospace,biomedical,automatic control technol-ogy and other production and living researches,all of them can be abstracted as high dimension,wide range mathematic differential equations to solve.However only a fewdifferential equation can calculate exact solution,the majority of the equations can't find out the exact solution.So people think of using approximate solution instead of exact solutions to solve the practical mathematical model problems,but the precision of the approximate solution directly affect the study of practical problems,so increas-ing the accuracy of approximate solution of differential equation has been praised by the scholars attention.Finite difference method is one of the most extensive numerical method which is used to answer differential equations,the basic idea is to use dif-ference equations with only contain a finite number of discrete unknown quantity to approximate instead continuous variable differential equations and the definite solution conditions,and the solution of differential equation as the approximate solutions of the differential equation of definite solution problems,discrete solution of differential equations with continuous differential equation solution,the smaller the error between the higher accuracy,and the smaller the impact on the solution actual problem.So the construction of a discrete differential equations is of great significance to the re-ality of production life.While for the difference algorithms of differential equations which involve less discrete grid points,don't need special treatments,higher precision,calculates have be come a hotspot of research scholars.At the same time,with the rapid development of computer industry,more and more people can be skilled in com-puter solving mathematical problems,which can use computer to do high-precision approximate solution for solving differential equations,greatly improved the accuracy of the approximate solution of differential equations,which made it more close to the actual problem.This paper mainly applied the basic difference formula to derive the four dimen-sional constant coefficient to reflect the close alternately difference scheme of diffusion equations,to pass the corresponding numerical experiments by MATLAB software,to verify the accuracy of the format.The main contents are as follows:The first chapter is the preface part,which introduces the research background of the reflection diffusion equation,and the basic knowledge of check grade,and the research process of reflection diffusion equations of scholars at home and abroad in recent years,and also briefly discuss the structure and main works of this paper.The second chapter,we provide four dimensional reaction-diffusion equation bound-ary value problem,establish a compact difference scheme and derive its corresponding truncation error expression,and then through the format deformation to derive the tight alternating direction difference scheme,and use Fourier's stability method to prove the stability and convergence of difference scheme.Then through the extrapola-tion method to work out the approximate solution of the format.Finally,the validity and accuracy of the proposed format are verified by calculation of a related numerical example.