Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 5Citation - Scopus: 10Conditioning and Error Analysis of Nonlocal Operators With Local Boundary Conditions(Elsevier Ltd., 2018) Aksoylu, Burak; Kaya, AdemWe study the conditioning and error analysis of novel nonlocal operators in 1D with local boundary conditions. These operators are used, for instance, in peridynamics (PD) and nonlocal diffusion. The original PD operator uses nonlocal boundary conditions (BC). The novel operators agree with the original PD operator in the bulk of the domain and simultaneously enforce local periodic, antiperiodic, Neumann, or Dirichlet BC. We prove sharp bounds for their condition numbers in the parameter δ only, the size of nonlocality. We accomplish sharpness both rigorously and numerically. We also present an error analysis in which we use the Nyström method with the trapezoidal rule for discretization. Using the sharp bounds, we prove that the error bound scales like O(h2δ−2) and verify the bound numerically. The conditioning analysis of the original PD operator was studied by Aksoylu and Unlu (2014). For that operator, we had to resort to a discretized form because we did not have access to the eigenvalues of the analytic operator. Due to analytical construction, we now have direct access to the explicit expression of the eigenvalues of the novel operators in terms of δ. This gives us a big advantage in finding sharp bounds for the condition number without going to a discretized form and makes our analysis easily accessible. We prove that the novel operators have ill-conditioning indicated by δ−2 sharp bounds. For the original PD operator, we had proved the similar δ−2 ill-conditioning when the mesh size approaches 0. From the conditioning perspective, we conclude that the modification made to the original PD operator to obtain the novel operators that accommodate local BC is minor. Furthermore, the sharp δ−2 bounds shed light on the role of δ in nonlocal problems.Article Citation - WoS: 16Citation - Scopus: 16Strang Splitting Method for Burgers-Huxley Equation(Elsevier Ltd., 2016) Çiçek, Yeşim; Tanoğlu, GamzeWe derive an analytical approach to the Strang splitting method for the Burgers-Huxley equation (BHE) ut+αuux-ε uXX=β(1-u)(u-γ)u. We proved that Srtang splitting method has a second order convergence in Hs(R), where Hs(R) is the Sobolev space and s is an arbitrary nonnegative integer. We numerically solve the BHE by Strang splitting method and compare the results with the reference solution.Article Citation - WoS: 17Citation - Scopus: 25Adaptive Vehicle Skid Control(Elsevier Ltd., 2006) Keçeci, Emin Faruk; Tao, GangIn this paper, adaptive vehicle skid control, for stability and tracking of a vehicle during slippage of its wheels without braking, is addressed. Two adaptive control algorithms are developed: one for the case when no road condition information is available, and one for the case when certain information is known only about the instant type of road surface on which the vehicle is moving. The vehicle control system with an adaptive control law keeps the speed of the vehicle as desired by applying more power to the drive wheels where the additional driving force at the non-skidding wheel will compensate for the loss of the driving force at the skidding wheel, and also arranges the direction of the vehicle motion by changing the steering angle of the two front steering wheels. Stability analysis proves that the vehicle position and velocity errors are both bounded. With additional road surface information available, the adaptive control system guarantees that the vehicle position error and velocity error converge to zero asymptotically even if the road surface parameters are unknown.Article Citation - WoS: 2Citation - Scopus: 1Errors Associated With Swelling in the Analysis of Polymer-Solvent Diffusion Measurements(Elsevier Ltd., 2005) Alsoy Altınkaya, SacideSorption curves are generated from a mathematical model which includes the influence of the polymer swelling for unsteady-state sorption of a vapor or liquid by a polymer. To investigate the simultaneous effects of the specific volumes of the polymer-penetrant pair and the difference between the final and initial equilibrium concentrations on the sorption curves, statistical experimental design approach is used. Simulation results obtained from the numerical solution of model equations are utilized to estimate the error that would occur if one simply evaluates the diffusion coefficient using the traditional formulas derived from the analytical solution of the sorption equation. An empirical expression is developed that describes the effects of the difference between the final and initial equilibrium concentrations and the specific volumes of the polymer and the penetrant on the magnitude of error in diffusivity associated with the use of one of these traditional formulas so called the initial slope method. The predictive ability of the regression model is tested by performing additional simulations not used in the regression analysis.