非线性抛物组的具有并行本性差分格式  

ON THE DIFFERENCE SCHEMES WITH INTRINSIC PARALLELISM FOR NONLINEAR PARABOLIC SYSTEMS

作　　者：周毓麟 

机构地区：[1]应用物理与计算数学研究所

出　　处：《数值计算与计算机应用》1995年第3期162-172,共11页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金;中物院基金

摘　　要：非线性抛物组的具有并行本性差分格式周毓麟（应用物理与计算数学研究所）ＯＮＴＨＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＷＩＴＨＩＮＴＲＩＮＳＩＣＰＡＲＡＬＬＥＬＩＳＭＦＯＲＮＯＮＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＳＹＳＴＥＭＳ￥ＺｈｏｕＹｕｌｉｎ（Ｉｎｓｔｉｔ...Abstract In the large scale scientific and engineering computations the effective parallel method and algorithm must be appropriate to the structure of the parallel computer with massive parallel processors. Some difference schemes of the problems need improving in order to suit the parallel computer. Some difference schemes themselves have the parallel character for direct use and for the naturally introduced numerical method and algorithm. The difference schemes having such a parallel charactar are called the difference schemes with intrinsic parallelism. The general difference schemes with intrinsic parallelism are constructed for the problems of quasilinear parabolic systems, nonlinear parabolic systems and two and three dimensional semilinear parabolic systems. For these schemes, the existence, uniqueness and the convergence of the discrete solutions are discussed and stated. Their stability with intrinsic parallelism is studied in the sense of the continuous dependence of the discrete solutions on the given data of the original problems. The key of these studies is the restriction conditions on the choice of the meshsteps for the space variables and the time variable.

关 键 词：非线性抛物组 并行本性 差分格式 偏微分方程 数值计算 

分 类 号：O241.82[理学—计算数学]