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Numerical approximate controllability for unidimensional parabolic integro-differential equations

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  • Zhao, Hengzhi
  • Zhang, Jiwei
  • Lu, Jing

Abstract

This paper discusses numerical solutions for the control functions of parabolic integro-differential equations under the assumption of approximate controllability. It is proved theoretically that the numerical solution for the control function converges to the exact solution, and the validity of the theory is demonstrated from different perspectives through four numerical simulation examples.

Suggested Citation

  • Zhao, Hengzhi & Zhang, Jiwei & Lu, Jing, 2023. "Numerical approximate controllability for unidimensional parabolic integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 575-596.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:575-596
    DOI: 10.1016/j.matcom.2022.09.001
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    References listed on IDEAS

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    1. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2017. "A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 272-282.
    2. A.M. Ramos & R. Glowinski & J. Periaux, 2002. "Nash Equilibria for the Multiobjective Control of Linear Partial Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 457-498, March.
    3. Mirzaee, Farshid & Samadyar, Nasrin, 2019. "Numerical solution based on two-dimensional orthonormal Bernstein polynomials for solving some classes of two-dimensional nonlinear integral equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 344, pages 191-203.
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