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    A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation

    Source: Journal of Computational and Nonlinear Dynamics:;2019:;volume( 014 ):;issue: 008::page 81005
    Author:
    Xu, Yong
    ,
    Liu, Qixian
    ,
    Liu, Jike
    ,
    Chen, Yanmao
    DOI: 10.1115/1.4043525
    Publisher: American Society of Mechanical Engineers (ASME)
    Abstract: We present a novel method to solve the Bagley-Torvik equation by transforming it into ordinary differential equations (ODEs). This method is based on the equivalence between the Caputo-type fractional derivative (FD) of order 3/2 and the solution of a diffusion equation subjected to certain initial and boundary conditions. The key procedure is to approximate the infinite boundary condition by a finite one, so that the diffusion equation can be solved by separation of variables. By this procedure, the Bagley-Torvik and the diffusion equations together are transformed to be a set of ODEs, which can be integrated numerically by the Runge-Kutta scheme. The presented method is tested by various numerical cases including linear, nonlinear, nonsmooth, or multidimensional equations, respectively. Importantly, high computational efficiency is achieved as this method is at the expense of linearly increasing computational cost with the solution domain being enlarged.
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      A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/4259329
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    contributor authorXu, Yong
    contributor authorLiu, Qixian
    contributor authorLiu, Jike
    contributor authorChen, Yanmao
    date accessioned2019-09-18T09:08:27Z
    date available2019-09-18T09:08:27Z
    date copyright5/13/2019 12:00:00 AM
    date issued2019
    identifier issn1555-1415
    identifier othercnd_014_08_081005
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4259329
    description abstractWe present a novel method to solve the Bagley-Torvik equation by transforming it into ordinary differential equations (ODEs). This method is based on the equivalence between the Caputo-type fractional derivative (FD) of order 3/2 and the solution of a diffusion equation subjected to certain initial and boundary conditions. The key procedure is to approximate the infinite boundary condition by a finite one, so that the diffusion equation can be solved by separation of variables. By this procedure, the Bagley-Torvik and the diffusion equations together are transformed to be a set of ODEs, which can be integrated numerically by the Runge-Kutta scheme. The presented method is tested by various numerical cases including linear, nonlinear, nonsmooth, or multidimensional equations, respectively. Importantly, high computational efficiency is achieved as this method is at the expense of linearly increasing computational cost with the solution domain being enlarged.
    publisherAmerican Society of Mechanical Engineers (ASME)
    titleA Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation
    typeJournal Paper
    journal volume14
    journal issue8
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4043525
    journal fristpage81005
    journal lastpage081005-5
    treeJournal of Computational and Nonlinear Dynamics:;2019:;volume( 014 ):;issue: 008
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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