Browsing by Author "Kaya, Mujdat"

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    A Method for the Numerical Solution of a Boundary Value Problem for a Linear Differential Equation with Interval Parameters
    (2019) Gasilov, Nizami A.; Kaya, Mujdat; AAN-9386-2020
    In many real life applications, the behavior of the system is modeled by a boundary value problem (BVP) for a linear differential equation. If the uncertainties in the boundary values, the right-hand side function and the coefficient functions are to be taken into account, then in many cases an interval boundary value problem (IBVP) arises. In this study, for such an IBVP, we propose a different approach than the ones in common use. In the investigated IBVP, the boundary values are intervals. In addition, we model the right-hand side and coefficient functions as bunches of real functions. Then, we seek the solution of the problem as a bunch of functions. We interpret the IBVP as a set of classical BVPs. Such a classical BVP is constructed by taking a real number from each boundary interval, and a real function from each bunch. We define the bunch consisting of the solutions of all the classical BVPs to be the solution of the IBVP. In this context, we develop a numerical method to obtain the solution. We reduce the complexity of the method from O(n(5)) to O(n(2)) through our analysis. We demonstrate the effectiveness of the proposed approach and the numerical method by test examples.
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    Simultaneous Reconstruction of the Source Term and The Surface Heat Transfer Coefficient
    (2015) Kaya, Mujdat; Erdem, Arzu; 0000-0003-4284-356X; AAD-3916-2020
    We study the problem of identifying unknown source terms in an inverse parabolic problem, when the overspecified (measured) data are given in form of Dirichlet boundary condition u(0,t)=h(t) and u(x,t)=q(x,t),(x,t, is an element of Omega(t1)degrees, where Omega(t1)degrees is an arbitrarily prescribed subregion. The main goal here is to show that the gradient of cost functional can be expressed via the solutions of the direct and corresponding adjoint problems. We prove Holder continuity of the cost functional and derive the Lipschitz constant in the explicit form via the given data. On the basis of the obtained results, we propose a monotone iteration process. Copyright (c) 2014 John Wiley & Sons, Ltd.