Finite Difference Domain Decomposition Algorithm For Numerical Solution Of The Heat Equation

In many fields of the natural science,many phenomenas are desribed by parabolic equation or equations. Heat equation is the most typical one of parabolical equations, which describes many physical-phenomenas,such as conduction,diffusion .etc.We are exprerienc-ing increasing tribulations by using the typical finite difference methods to solve those parabolical-equations. Hence , it is very meaningful to divide the domain over which the problem is defined into subdomains,and solve the subdomain problem in parallel.This thesis will be divided into 4 chapters.The developments of the domain decomposition algorithm and finite Difference domain decomposition algorithm for numerical solution of the heat equation have been introduced in Chapter l,in which main work of this paper is also described.In Chapter 2,first we give the error estimate results on the different solutions of domain decomposition algorithm .Then a new decomposition algorithm for the heat equation with the first class boundary-dondotion is also developed by using Saul'yev asymmetric schemes at the interface points,and the prior error estimates of the approximate solution is obtained.The results of the new algorithm are compared with that of the algorithm developed by C.N.Dwson.At last ,we use this new algorithm to solve the heat equation with the second class boundary-dondotion, which is more useful by taking a numerical example. In Chapter 3,a new finite difference decomposition algorithm for the two-dimensional heat equation is developed by using MA Ming-shu's group's new schemes with parameter 77 at interface points,relaxed stability condition, and the error bound of the approximate solution are obtained.The results of the new algorithm are compared with that of the algorithm in [1],and we can get a better error bound at interface points with optimal parameters . First, a brief introduction is given to the domain decomposition algorithm. Domain decomposition algorithm is a new effective method developed to solve the partial differential equation in parallel. Lots of attention is paid to the domain decomposition algorithm for its numerous advantages. Mathematicians from the whole world including America, Russia, France etc. are interesting in the method and developing their genres. According to their different decomposition of the computation domain,...