THE UNCONDITIONAL STABILITY OF PARALLEL DIFFERENCE SCHEMES WITH SECOND ORDER CONVERGENCE FOR NONLINEAR PARABOLIC SYSTEM  

作　　者：Yuan Guangwei Sheng Zhiqiang Hang Xudeng 

机构地区：[1]Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing P.O.Box 8009, Beijing 100088, China

出　　处：《Journal of Partial Differential Equations》2007年第1期45-64,共20页偏微分方程（英文版）

基　　金：The project is supported by the Special Funds for Major State Basic Research Projects 2005CB321703, the National Nature Science Foundation of China （No. 10476002, 60533020）.

摘　　要：For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the （Dirichlet） boundary condition for solving the sub-domain problems. Then the values in the sub-domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.

关 键 词：Parallel difference scheme nonlinear parabolic system unconditional stability second order convergence. 

分 类 号：O241.82[理学—计算数学] O241.84[理学—数学]