Kasemsuwan, Jaipong

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Kasemsuwan, Jaipong
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Email
jaipong.ka@kmitl.ac.th

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    Item type:Publication,
    Differential transformation method for circular membrane vibrations
    (2019-01-01)
    Kasemsuwan, Jaipong
    ;
    Sabau, Sorin Vasile
    ;
    Somboon, Uraiwan
    The purpose of this research is to present the steps of one-dimensional differential transformation method (DTM) to find the series solutions for the vibrations of a circular membrane under the specified initial and boundary conditions. The problems will be studied in the both cases of vibrations depending only on radius and of the vibrations depending on both radius and angle. We illustrate four examples of problems which the exact solutions can be solve analytically and compare them to the DTM results, to show that the DTM is reliable and of high accuracy. This work shows that the DTM is easier to use than the analytical method from the point of view of programming.
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    New transform formulae for differential transformation method with applications to the nonlinear plane autonomous systems
    (2020-01-01)
    Somboon, Uraiwan
    ;
    Kasemsuwan, Jaipong
    ;
    Sabau, Sorin V.
    This work presents a new derivation technique for new differential transform formulae of a product of composite functions. The new formulae are applied to nonlinear plane autonomous systems to demonstrate their efficiency and reliability. The approximate series solutions estimated by the differential transform method (DTM) and the multistep differential transform method (MsDTM) are then compared with the flow direction of the vector fields defined by the original system and an analytical solution calculated by the phase-plane method. We found that the MsDTM results are in better agreement with the analytical solution than the DTM ones. Moreover, the MsDTM can be applied to systems whose analytical solutions are unobtainable. The approximate solutions by the MsDTM have the same direction to the flow of the vector field of the system. It follows that the proposed new formulae are reliable and efficient.