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

M. Zarepour () and G. B. Loghmani ()
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M. Zarepour: Yazd University
G. B. Loghmani: Yazd University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 3, No 12, 933-948

Abstract: 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.

Keywords: Ordinary differential equations; Integro-differential equations; Parametric optimal control (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0019-4

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