In recent years, domain decomposition method for solving partial differential equations has become one of the effective method, domain decomposition method to complex or large-scale decomposition into several overlapping or non-overlapping sub-regions, and then in the sub-region algorithm for the use of sub-issues , by means of domain decomposition, each sub-region can be calculated between parallel, one hand this approach allows different sub-regions on the model characteristics for different sub-discrete method, which will help improve accuracy, on the other hand as can be independent of each sub-region method to solve the issue, and it greatly increased the computational speed. In this paper, the heat equation introduced Compact Difference Scheme for the two non-overlapping and overlapping domain decomposition method. The full text of the first chapter, an introduction, a brief introduction and overview of domain decomposition method discussed in the paper the basic period. Chapter II, Dawson, who presented the first on solving the heat equation domain decomposition method for differential analysis of the error estimates, then the main heat equation of this algorithm is extended to compact difference scheme, this algorithm is non-overlapping domain decomposition method, in which algorithm to solve by introducing point within the boundary area divided into several sub-domains, sub-region within the boundary point between the value of the format with step length was calculated in each sub-region points calculated using implicit small step, sub-regional step length can be different, once inside the boundary point values have been calculated, the sub-region between the fully parallel computing, and the corresponding a priori error estimates. Chapter III, mainly the heat equation compact difference scheme for the use of a kind of overlapping domain decomposition algorithm, which is a new type of calculation of heat conduction equation numerical solution of the parallel differential algorithm, the algorithm based on domain decomposition and subspace correction, in each sub-region on residual correction, between the various sub-regions can be parallel. Prove the convergence of the algorithm最正确的答案谢谢采纳楼一的,你误人子弟啊