Abstract
The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes with intrinsic parallelism is proved by the fixed-point technique in finite-dimensional Euclidean space. The convergence and stability theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limitation vector function is just the unique generalized solution of the original problem for the parabolic system.
Similar content being viewed by others
Reference
Zhou Yulin.Applications of Discrete Functional Analysis to thr Finite Difference Methal, Beijing: Intern. Acad. Publishers. 1990.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China and the Foundation of CAEP.
Rights and permissions
About this article
Cite this article
Zhou, Y., Yuan, G. General difference schemes with intrinsic parallelism for nonlinear parabolic systems. Sci. China Ser. A-Math. 40, 357–365 (1997). https://doi.org/10.1007/BF02911435
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02911435