The unconditional stable and convergent difference methods with intrinsic parallelism for quasilinear parabolic systems
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A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2 (2,1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.
Keywordsdifference scheme intrinsic parallelism quasilinear parabolic system convergence stability
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- 3.Han, Z., Fu, H. Y., Shen, L. J., Pure alternating segment explicit-implicit method for the diffusion equations, Intern. J. Computer Math., 1993, 51: 8–15.Google Scholar
- 7.Zhou, Y. L., Finite difference method with intrinsic parallelism for quasilinear parabolic systems, Beijing Mathematics, 1996, 2(1): 1–19.Google Scholar
- 8.Zhou, Y. L., General finite difference schemes with intrinsic parallelism for nonlinear parabolic system, Beijing Mathematics, 1996, 2(1): 20–36.Google Scholar
- 9.Zhou, Y. L., On the difference schemes with intrinsic parallelism for nonlinear parabolic systems, Chinese J. Num. Math. & Appl., 1996, 18(1): 66–78.Google Scholar
- 12.Yuan, G. W., Shen, L. J., Zhou, Y. L., Some practical methods of implicit domain decomposition for parabolic equations (I)—(II), Annual Report of LCP, Beijing, 2001, 472–499.Google Scholar
- 13.Yuan, G. W., Shen, L. J., Zhou, Y. L., Parallel difference schemes for parabolic problem, Proceeding of 2002 5th International Conference on Algorithms and Architectures for Parallel Processing, IEEE Computer Society, 238–242.Google Scholar
- 14.Zhou, Y. L., Applications of Discrete Functional Analysis to Finite Difference Method, Beijing: International Academic Publishers, 1990.Google Scholar