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Alipour, Maryam, Soradi Zeid, Samaneh. (1401). Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method. سامانه مدیریت نشریات علمی, 11(1), 52-64. doi: 10.22034/cmde.2022.50643.2100
Maryam Alipour; Samaneh Soradi Zeid. "Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method". سامانه مدیریت نشریات علمی, 11, 1, 1401, 52-64. doi: 10.22034/cmde.2022.50643.2100
Alipour, Maryam, Soradi Zeid, Samaneh. (1401). 'Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method', سامانه مدیریت نشریات علمی, 11(1), pp. 52-64. doi: 10.22034/cmde.2022.50643.2100
Alipour, Maryam, Soradi Zeid, Samaneh. Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method. سامانه مدیریت نشریات علمی, 1401; 11(1): 52-64. doi: 10.22034/cmde.2022.50643.2100

Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method

Computational Methods for Differential Equations
مقاله 5، دوره 11، شماره 1، فروردین 2023، صفحه 52-64    اصل مقاله (542.92 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50643.2100
نویسندگان
Maryam Alipour1؛ Samaneh Soradi Zeid* 2
1Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
2Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran.
چکیده
In this paper, we introduce a new direct scheme based on Dickson polynomials and collocation points to solve a class of optimal control problems (OCPs) governed by Volterra integro-differential equations namely Volterra integro-OCPs (VI-OCPs). This topic requires to calculating the corresponding operational matrices for expanding the solution of this problem in terms of Dickson polynomials. Further, the highlighted method allows us to transform the VI-OCP into a system of algebraic equations for choosing the coefficients and control parameters optimally. The error estimation of this technique is also investigated which given the high efficiency of the Dickson polynomials to deal with these problems. Finally, some examples are brought to confirm the validity and applicability of this approach in comparison with those obtained from other methods. 
کلیدواژه‌ها
Dickson polynomials؛ Optimal control problem؛ Volterra integro-differential equation؛ Algebraic equations؛ Collocation points؛ Error estimation
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