The unconditional stable and convergent difference methods with intrinsic parallelism for quasilinear parabolic systems

查看全文 作　　者：ZHOU Yulin;YUAN Guangwei;SHEN Longjun Laboratory of Computational Physics, Center of Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

出　　处：《Science China Mathematics》索引2004年第47卷第3期,共20页

基　　金：This work was supported by China“National Key Program for Developing Basic Sciences”G1999032801;the National Natural Science Foundation of China(Grant No.19932010);the Foundation of CAEP(20020652). 摘　　要：A kind of the general finite difference schemes with intrinsicparallelism for the boundary value problem of the quasilinearparabolic system is studied without assuming heuristically thatthe original boundary value problem%for the quasilinear parabolic systemhas the unique smooth vector solution. By the method of a prioriestimation of the discrete solutions of the nonlinear differencesystems, and the interpolation formulas of the various norms ofthe discrete functions and the fixed-pointtechnique in finite dimensional Euclidean space, the existence anduniqueness of the discrete vector solutions of the nonlineardifference system with intrinsic parallelismare proved. Moreover the unconditional stability ofthe general finite difference schemes with intrinsic parallelismis justified in the sense of the continuous dependence of thediscrete vector solution of the difference schemes on the discretedata of the original problems in the discrete W(2,1)2 norms. Finally the convergence of the discrete vector solutions ofthe certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved. 关键词：difference scheme, INTRINSIC parallelism,quasilinear PARABOLIC system, convergence, stability.

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The unconditional stable and convergent difference methods with intrinsic parallelism for quasilinear parabolic systems

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