IJPAM: Volume 66, No. 2 (2011)

ON THE NUMERICAL INTEGRATION OF
ONE NONLINEAR PARABOLIC EQUATION

Mikheil Tutberidze
Ilia State University
3/5 Kakutsa Cholokashvili Ave., Tbilisi, 0162, GEORGIA
e-mail: [email protected]


Abstract.In the present paper the difference analogue of the initial-boundary value problem to one nonlinear parabolic equation is considered. In certain conditions the convergence of the solution of the difference analogue to the solution of source problem is proved. For the same difference analogue the comparison theorem is proved and the uniqueness of the solution is obtained. The iteration process for finding of the solution of difference analogue is constructed and in certain conditions its convergence is obtained.

Received: November 4, 2010

AMS Subject Classification: 65M06

Key Words and Phrases: difference analogue, comparison theorem, partial differential equation, convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 2