Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: In this thesis, a numerical method for solving nonlinear partial differential equations and system equations in a class of discontinuous functions which are often met in practice is suggested method is briefly investigated in section 2.1 and applied to an one-dimensional problem of first ordered partial equation with a periodical boundary condition. In section 2.3 the mentioned method has been developed to a two- dimensional initial and boundary value problem which is of first ordered nonlinear partial differential equation in a class of discontinuos functions. For this aim, the exact solution is structured and some properties of it are studied.In section 2.4 the suggested method is further developed to a system of nonlinear partial differential equations in a class of discontinuos functions which arise in gas-dynamics problem, and also in many field of hydrodynamics. In the final section of thesis, the method is studied further for one- dimensional, second ordered nonlinear wave equation in a class of discontinuos functions.Each differential operator used in each section of the thesis is factorized. A special auxiliary problem in a class of kernel of one of the factorized operators is introduced. These auxiliary problems have some advantages over the main problem that provide us to develop efficient and economical algorithms from computational point of view. And the suggested method makes it possible to find the the position and time evaluation of a shock wave which originates from the physical nature of the problem.Key Words: Nonlinear Wave Distribution, Shoch Wave , Weak Solution, Numerical Method in a Class of Discontinuos Functions, Subsonic and Transonic Flow, Computational Hydrodynamics, Numerical Modelling. | |||||||||||||||||||||