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

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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.

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Acknowledgements

The authors are highly grateful to the referee(s) for their valuable comments and suggestions for improving the paper.

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  1. Department of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, Iran

    M. Zarepour & G. B. Loghmani

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  1. M. Zarepour
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  2. G. B. Loghmani
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Correspondence to G. B. Loghmani.

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Zarepour, M., Loghmani, G.B. Numerical Solution of Arbitrary-Order Ordinary Differential and Integro-Differential Equations with Separated Boundary Conditions Using Optimal Control Technique. J Optim Theory Appl 154, 933–948 (2012). https://doi.org/10.1007/s10957-012-0019-4

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