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    Öğe
    Analysis of an Undamped Mass-Spring System with Generalized Piecewise Constant Argument
    (L and H Scientific Publishing, LLC, 2023) Akhmet, Marat; Çinçin, Duygu Aruğaslan; Özkan, Zekeriya
    In this study, we consider an undamped mass-spring system that experiences piecewise constant forces and analyze the solutions of this system. We investigate the solutions of undamped mass-spring system by using the method of steps. In addition to investigating the solutions, stability and convergency analyses are performed for the solutions of nonhomogeneous undamped mass-spring system. The results are stated in terms of the parameters of the systems. Simulations are given to illustrate and support the findings for different values of the parameters.
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    Öğe
    New results on a partial differential equation with general piecewise constant argument
    (Matematikçiler Derneği, 2023) Akhmet, Marat; Aruğaslan Çinçin, Duygu; Özkan, Zekeriya
    here have been very few analyses on partial differential equations with piecewise constant arguments and as far as we know, there is no study conducted on heat equation with piecewise constant argument of generalized type. Motivated by this fact, this study aims to solve and analyse heat equation with piecewise constant argument of generalized type. We obtain formal solution of heat equation with piecewise constant argument of generalized type by separation of variables. We apply the Laplace transform method using unit step function and method of steps on each consecutive intervals. We investigate stability, oscillation, boundedness properties of solutions.