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An optimal control approach for arbitrary order singularly perturbed boundary value problems | ||
| Iranian Journal of Science | ||
| مقاله 8، دوره 37، شماره 3.1، آذر 2013، صفحه 379-388 اصل مقاله (114.37 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2013.1637 | ||
| نویسندگان | ||
| M. Zarepour1؛ G. B. Loghmani* 2 | ||
| 1Department of Mathematics, Yazd University, P.O. Box: 89195-741 Yazd, Iran | ||
| 2Department of Mathematics, Yazd University | ||
| چکیده | ||
| The aim of this paper is to introduce a new approach for obtaining the numerical solution of singulary perturbed boundary value problems based on an optimal control technique. In the proposed method, first the mentioned equations are converted to an optimal control problem. Then, control and state variables are approximated by Chebychev series. Therefore, the optimal control problem is reduced to a parametric optimal control problem (POC) subject to algebric constraints. Finally, the obtained POC is solved numerically using an iterative optimization technique. In this method, a new idea is proposed which enables us to apply the new technique for almost all kinds of singularly perturbed boundary value problems. Some numerical examples are solved to highlight the advantages of the proposed technique. | ||
| کلیدواژهها | ||
| Singularly perturbed boundary value problem؛ parametric optimal control؛ Optimal control problem | ||
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