Yazar "Sahin, E. Ilhan" seçeneğine göre listele

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    Finite Differences Method for the First Order 2-D Partial Equation
    (Springer-Verlag Berlin, 2013) Rasulov, Mahir; Sahin, E. Ilhan; Soguksu, M. Gokhan
    In this study a new method for finding exact solution of the Cauchy problem subject to a discontinuous initial profile for the two dimensional scalar conservation laws is suggested. For this aim, first, some properties of the weak solution of the linearized equation are investigated. Taking these properties into consideration an auxiliary problem having some advantages over the main problem is introduced. The proposed auxiliary problems also permit us to develop effective different numerical algorithms for finding the solutions. Some computer experiments are carried out.
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    Investigating the Dynamics of Traffic Flow on a Highway in a Class of Discontinuous Functions
    (Springer-Verlag Berlin, 2015) Sinsoysal, Bahaddin; Bal, Hakan; Sahin, E. Ilhan
    This work is devoted to finding a solution of Riemann problem for the first order nonlinear partial equation which describes the traffic flow on highway. When rho(l) > rho(r), the solution is presented as a piecewise continuous function, where rho(l) and rho(r) are the densities of cars on the left and right side of the intersection respectively. On the contrary case, a shock of which the location is unknown beforehand arises in the solution. In this case, a special auxiliary problem is introduced, the solution of which makes it possible to write the exact solution showing the locations of shock. For the realization of the proposed method, the parameters of the flow are also found.