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Öğe Grid method for solution of 2D Riemann type problem with two discontinuities having an initial condition [???????? ????? ??i ??i?i?i ??? ????? ????i ??i ??????i ?????i ?????i? ??? ??i?i] [???????? ????? ??????? ????????? ?????? ???? ?????? ? ????? ?????????, ???????? ????????? ?????????](E.A.Buketov Karaganda State University Publish House, 2021) Sinsoysal B.; Rasulov M.; Yener O.This study aims to obtain the numerical solution of the Cauchy problem for 2D conservation law equation with one arbitrary discontinuity having an initial profile. For this aim, a special auxiliary problem allowing to construct a sensitive method is developed in order to get a weak solution of the main problem. Proposed auxiliary problem also permits us to find entropy condition which guarantees uniqueness of the solution for the auxiliary problem. To compare the numerical solution with the exact solution theoretical structure of the problem under consideration is examined, and then the interplay of shock and rarefaction waves is investigated. © Bulletin of the Karaganda University. Mathematics Series.Öğe Numerical simulation of initial and initial-boundary value problems for traffic flow in a class of discontinuous functions(2006) Rasulov M.; Sinsoysal B.; Hayta S.In this paper, a new method for obtaining a numerical solution of the Cauchy and initial- boundary problems for a first order nonlinear partial differential equation which describes the traffic flow on highway is suggested. For this purpose, the first and second type auxiliary problems having some advantages over the main problem, but equivalent to it, are introduced and some properties of the numerical solution are studied. Some computer experiments have been carried out.Öğe One method to prove of existence weak solution of a mixed problem for 2D parabolic equations(Elsevier B.V., 2020) Sinsoysal B.; Rasulov M.In this study using the residue method the solution of the first type mixed problem for 2D linear parabolic equation in the bounded cylinder of the Euclidean space R3(x,y,t) is obtained in explicit form. When the smoothness of initial data does not permit to construct of the classical solution then it is necessary to extend the concept of classical solution. Based on the examined problem is proved that the obtained solution is a weak solution too. The use of this proof method to prove the existence of a weak solution can be applied to prove the existence of weak solutions for the more general problem with non-self-adjoint and even that contains higher-order derivative with respect to t in the boundary condition. © 2020 The Author(s)
