Open AccessMATHEMATICAL MODELING OF THE BOUNDARY CONDITIONS OF THE OCEANALOGY WITH THE HELP PHOTO AREA METHOD
Author(s) -
L.M. Tukenova
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-4.1728-7901.11
Subject(s) - convergence (economics) , domain (mathematical analysis) , stability (learning theory) , boundary value problem , rate of convergence , mathematics , boundary (topology) , nonlinear system , differential equation , computer science , mathematical optimization , mathematical analysis , physics , computer network , channel (broadcasting) , quantum mechanics , machine learning , economics , economic growth
Mathematical models of oceanology are equations of the Navier-Stokes type, the construction of stable effective algorithms for their solution is associated with certain difficulties due to the well-known problems of setting boundary conditions, the presence of integro-differential relations, etc. In practice, when solving problems of oceanology, finitedifference methods are widely used, but there are no works in the literature devoted to theoretical studies of the stability and convergence of the algorithms used. In most cases, stability and convergence tests are established through computational experiments. Therefore, we believe that the development and mathematical substantiation of converging methods for solving the system of oceanology equations are urgent problems of computational mathematics. The paper studies variants of the fictitious domain method for a nonlinear ocean model. An existence theorem for the convergence of solutions to approximate models obtained using the fictitious domain method is investigated. An unimprovable estimate of the rate of convergence of the solution of the fictitious domain method is derived.