Riemann problem and its applications

Comparative practicality criterions of Gakhov and Muskhelishvili methods are studied in linewith the absolute solution of some non-homogeneous Riemann problems. This study aims tosolve some classical type Riemann boundary value problems by using Gakhov andMuskhelishvili methods. It is endeavored to find answers to the following questions byfinding out the absolute solutions of these problems:If we do not use numerical solution methods, to what extent these methods can beregarded as useful to obtain absolute solutions?Can the contour given by the problem be a factor in the selection of these methods?How does the problem?s coefficient affect the method selection?In which cases can the problem?s free-term be effective in method selection?Are the additional boundary conditions effective in method selection?The secondary focus of this paper is exceptional cases and various generalizations of theRiemann boundary value problem.Keywords: Non-homogeneous Riemann problem, Gakhov?s method, Muskhelishvili?smethod, full solution of the Riemann problem, canonical solution of the Riemann problem,direct solution of the Riemann problem.JURY:1.Yrd.Doç.Dr. Coşkun GÜLER2.Prof.Dr. Mustafa S VR Date: 19.07.20063.Prof.Dr. Mustafa BAYRAM Page: 132