数值计算与计算机应用 1995, 16(3 ) 162-172 DOI:     ISSN: 1000-3266 CN: 11-2124/TP

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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

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...

关键词

ON THE DIFFERENCE SCHEMES WITH INTRINSIC PARALLELISM FOR NONLINEAR PARABOLIC SYSTEMS

Zhou Yulin(Institue of Applied Physics and Computational Mathematics )

Abstract:

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.

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