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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 A finite differences method for a two-dimensional nonlinear hyperbolic equation in a class of discontinuous functions(Elsevier Science Inc, 2003) Rasulov, M; Coskun, E; Sinsoysal, BA numerical scheme is proposed for a scalar two-dimensional nonlinear first-order wave equation with both continuous and piecewise continuous initial conditions. It is typical of such problems to assume formal solutions with discontinuities at unknown locations, which justifies the search for a scheme that does not rely on the regularity of the solution. To this end, an auxiliary problem which is equivalent to, but has more advantages then, the original system is formulated and shown that regularity of the solution of the auxiliary problem is higher than that of the original system. An efficient numerical algorithm based on the auxiliary problem is derived. Furthermore, some results of numerical experiments of physical interest are presented. (C) 2002 Elsevier Science Inc. All rights reserved.Öğe Finite differences method for shallow water equations in a class of discontinuous functions(Elsevier Science Inc, 2005) Rasulov, M; Aslan, Z; Pakdil, OIn this study a finite difference method for solving initial boundary value problem for the one-dimensional nonlinear system of differential equations describing shallow water flows in a class of discontinuous functions is suggested. In order to find the numerical solution of the problem, known as main problem, a special auxiliary problem is introduced. The degree of smoothness of the solution of the auxiliary problem is higher than the smoothness of the solution of the main problem. Moreover, the suggested auxiliary problem makes it possible to write out the effective and higher order numerical algorithms. Some results of numerical experiments are demonstrated. (C) 2003 Elsevier 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 The finite differences scheme for the first order system of nonlinear differential equations in a class of discontinuous functions(Elsevier Science Inc, 2004) Rasulov, MIn this paper, the finite difference scheme for solving the Cauchy problem for the simplified Euler system in a class of discontinuous 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 superior to the main problem in terms of obtaining the solution is introduced, and the solutions of this auxiliary problem are smoother than the solutions of the main problem. Additionally, the auxiliary problem provides to develop effective and economical algorithms. (C) 2003 Elsevier Inc. All rights reserved.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.Öğe Numerical solution of one dimensional filtration of three phase compressible fluid through porous medium in a class of discontinuous functions(Elsevier Science Inc, 2005) Rasulov, MA numerical method is proposed for a system of nonlinear partial differential equations which describe the flow of three phased mixture in a porous medium taking the capillary pressure into account. For this aim, firstly, by splitting the system of differential equations with respect to physical factors, a special auxiliary problem is introduced. Then, on the basis of this auxiliary problem, the finite differences method for solving the solution of the main problem in a class of discontinuous functions is developed, which accurately describes the whole properties of the physical problem at interest. Some results of the numerical experiments of physical interest are presented. (c) 2004 Elsevier Inc. All rights reserved.
