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Öğe Finite difference method for solving boundary initial value problem of a system hyperbolic equations in a class of discontinuous functions(Elsevier Science Inc, 2004) Rasulov, M; Karaguler, T; Sinsoysal, BIn this paper, a finite-difference method for solving boundary initial value problem of nonlinear system equations of hyperbolic type in a class of discontinuous functions is suggested. In order to obtain the numerical solution of the Main problem in a class of discontinuous functions the auxiliary problem is introduced. The degree of smoothness of the solution of the auxiliary problem is higher than of smoothness of the solution of the main problem. Furthermore, the suggested auxiliary problem lets us write out effective and-higher order numerical algorithms. The solutions obtained from these algorithms represent the physical nature of the problem with a high accuracy. Some numerical experiments are carried out by using the auxiliary problem. (C) 2003 Elsevier Inc. All rights reserved.Öğe Finite difference schemes for solving system equations of gas dynamic in a class of discontinuous functions(Elsevier Science Inc, 2003) Rasulov, M; Karaguler, TIn this paper, the difference scheme for solving nonlinear system of equations of gas dynamic problems in a class of discontinuous functions is investigated. Firstly, for some simple cases, the nature of solution of the differential equations describing one-dimensional, constant pressure, and isentropic flow of compressible fluids are considered. It has been proved that the solution of this system equations has discontinuous points whose positions are unknown beforehand. In order to obtain the solution of the main problem in a class of discontinuous functions, the auxiliary problem is suggested. The degree of differentiability of the solution of the auxiliary problem is higher than the degree of differentiability of solution of the main problem. Furthermore, the suggested auxiliary problem provides to write out effective and higher order numerical algorithms. The solutions obtained from these algorithms represent the physical nature of the problem with a high accuracy. Some properties of numerical solution are also investigated. Additionally, some numerical experiments are carried out by means of using the auxiliary problem. (C) 2002 Elsevier Science Inc. All rights reserved.Öğe Finite differences scheme for the Euler system of equations in a class of discontinuous functions(Springer-Verlag Berlin, 2005) Rasulov, M; Karaguler, TIn this paper, the finite difference scheme for solving the Cauchy problem for the simplified Euler system in a class of discountinuous functions, which describes irrational flow of fluid by neglecting the viscosity and temperature effects is investigated. For this purpose, firstly the Euler system is decomposed with respect to its coordinates. Then an auxiliary problem which is superiour to the main problem in terms of obtaining the solution is introduced, and shown that the solutions of this auxiliary problem are smoother than the solutions of the main problem. Additionally, the auxiliary problem provides to develop effective and efficient algorithms.Öğe Numerical solution of Cauchy problem for second order nonlinear wave equation with changeable type in a class of discontinues functions(Elsevier Science Inc, 2004) Rasulov, M; Karaguler, T; Sinsoysal, BIn this paper, a special numerical method for the solution of second order nonlinear wave equation with changeable type in a class of discontinues functions, which accurately describe the physical properties of the problem of interest is suggested. For this, first, an auxiliary problem having some advantages over the main problem is introduced. Since, the differentiable property of the solution of the auxiliary problem is twice higher than the differentiability of the solution of the main problem, the application of classical methods to the auxiliary problem can be easily performed. Some economic algorithms are proposed for obtaining a numerical solution of the auxiliary problem, and by using the solution of the auxiliary problem, the numerical solution of the main problem is also found. In order to show the effectiveness of the suggested algorithms some comparisons between the exact solution and the numerical solution are made. (C) 2002 Elsevier Inc. All rights reserved.
