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Trajectory Controllability of Second Order Nonlinear Integro-Differential System: An Analytical and a Numerical Estimation

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Abstract

In this short article we have discussed trajectory controllability of the second order nonlinear integro-differential system by using theory of monotone operators and tools of cosine operators. We will then describe a general method for computing numerical approximations to control functions. We will illustrate this method with a nonlinear integro-differential equations and a nonlinear hyperbolic equation in one and two spatial dimensions.

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Acknowledgments

First author expresses his thanks to Grant-In-Aid, Jackson-Hope grant of VMI (JH 2014) for kind support. Authors express their gratitude to all three anonymous referees for valuable comments and suggestions which are helpful to modify the manuscript.

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Authors and Affiliations

  1. Department of Applied Mathematics, Virginia Military Institute, 431 Mallory Hall, Lexington, VA, 24450, USA

    Dimplekumar Chalishajar

  2. Department of Mathematics and Statistics, James Madison University, Roop Hall, Harrisonburg, VA, 22801, USA

    Heena Chalishajar

Authors
  1. Dimplekumar Chalishajar
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  2. Heena Chalishajar
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Correspondence to Dimplekumar Chalishajar.

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Chalishajar, D., Chalishajar, H. Trajectory Controllability of Second Order Nonlinear Integro-Differential System: An Analytical and a Numerical Estimation. Differ Equ Dyn Syst 23, 467–481 (2015). https://doi.org/10.1007/s12591-014-0220-z

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  • DOI: https://doi.org/10.1007/s12591-014-0220-z

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