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Numerical Solution of Arbitrary-Order Ordinary Differential and Integro-Differential Equations with Separated Boundary Conditions Using Optimal Control Technique

Author

Listed:
  • M. Zarepour

    (Yazd University)

  • G. B. Loghmani

    (Yazd University)

Abstract

In this paper, a new method for solving arbitrary order ordinary differential equations and integro-differential equations of Fredholm and Volterra kind is presented. In the proposed method, these equations with separated boundary conditions are converted to a parametric optimization problem subject to algebraic constraints. Finally, control and state variables will be approximated by a Chebychev series. In this method, a new idea has been used, which offers us the ability of applying the mentioned method for almost all kinds of ordinary differential and integro-differential equations with different types of boundary conditions. The accuracy and efficiency of the proposed numerical technique have been illustrated by solving some test problems.

Suggested Citation

  • M. Zarepour & G. B. Loghmani, 2012. "Numerical Solution of Arbitrary-Order Ordinary Differential and Integro-Differential Equations with Separated Boundary Conditions Using Optimal Control Technique," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 933-948, September.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0019-4
    DOI: 10.1007/s10957-012-0019-4
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    References listed on IDEAS

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    1. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
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    1. Zarepour, Mazyar & Loghmani, Ghasem Barid, 2021. "Numerical solution of arbitrary-order linear partial differential equations using an optimal control technique," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 77-96.

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