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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 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 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.
