A Domain Decompostion Algorithm For Parabolic Equation

In many fields of the natural science, many phenomenons are described by parabolic equation or equations. Heat equation is the most typical one of parabolical equations, which describes many physical-phenomenons, such as conduction, diffusion.etc. We are experiencing increasing tribulation by us-ing the typical finite difference methods to solve those parabolical-equations. As a new effective algorithm to solve parabolic equation, domain decomposi-tion algorithm is attracting more and more attentions. The algorithm divides the computational domain into several sub-domains, and solves the original problems into the sub-domains. On the hand, owing to using different discrete methods in different sub-domains according to the characters of the sub-model, the algorithm will improve the computational accuracy,especially for the sub-domains whose solutions change largely; On the other hand, the algorithm can solve differential equation in every sub-domain independently, which improve the Computational speed greatly.This thesis will be divided into 3 chapters,organized as follows:In chap-ter 1, the developments of the domain decomposition and the algorithm for numerical solution of the parabolical equation have been introduced, and the main work of this paper is also described. In chapter 2, we take different time step length at odd and even time step. Then a new decomposition al-gorithm for the heat equation is developed, 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.Dawson. In chapter 3. On the basis of C-N algorithm, we developed a new asymmetric schemes. Then a new decomposition algorithm for the heat equation is developed, and the prior error estimates of the approximate solution is obtained.