Abstract:
The lot of problems of science and the techniques, studied by means of mathematical modeling and computing experiment, is reduced to the solution of systems of the multidimensional equations of parabolic type with partial derivatives. Such problems concern: distribution of heat to the continuum, processes of transfer of substances, diffusion and many fundamental problems of natural sciences, ecology and etc.
The problem with first sort boundary conditions for systems of equations of parabolic type, containing the mixed derivatives will be considered. The two-layer and three-layer factorized schemes are constructed. The received algorithms can be effectively used for multiprocessor computing systems.
For considered difference schemes aprioristic estimations in norm of net space on a layer are obtained, on which basis the convergence of solution of the difference schemes to the solution of initial problem is proved.

Brief Biography of the Speaker:
Prof. Hamlet Meladze has the scientific degree of D.Sc. in Mathematical Modeling and Numerical Mathematics (The Institute of Mathematical Modeling of Academy of Sciences of Russia). Field of his scientific interests: the numerical methods for solving of linear and nonlinear differential equations with partial derivatives; mathematical and computer modeling, parallel algorithms, fuzzy mathematics and etc.
He is head of department of informatics in Institute of Computational Mathematics (www.acnet.ge/icm) and the head of direction of Computer sciences in St. Andrew the First Called Georgian University (www.sangu.ge). Throughout many years H.Meladze works as Professor, the Head of Department of Computer Software and Information Technologies (1978-2006) and the Dean of faculty of applied mathematics and computer sciences (1993-1999) in Iv.Javakhishvili Tbilisi State University. He has the scientific award of Tbilisi state University for the best manual, also different scientific and governmental awards, medals and diplomas.
Prof. H.Meladze has about 126 scientific papers, is author of 11 books in numerical methods and informatics, editor of several books.
Prof. H.Meladze was head of project from Georgian side in various international grants.
He is Editor-in-Chief of electronics scientific journal “Computer sciences and telecommunications” (http://gesj.internet-academy.org.ge/en/title_en.php?b_sec=&section_l=comp), associate editor of journal “Applied Mathematics, Informatics and Mechanics” (http://www.viam.science.tsu.ge/Ami/Main.htm), the member of editorial board of journal “Transactions Automated Control Systems” (Georgian Technical University), also the member of editorial board of several international scientific journals.
Prof. H. Meladze was the member of international program committee and the participant of many international scientific conferences.
Prof. Hamlet Meladze is the member of European Academy of Sciences, vice-president of Academy of Natural Sciences of Georgia, the member of Academy of Educational Sciences of Georgia.