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

Document Type : Research Paper


1 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.

2 Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran.


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. 


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Volume 11, Issue 1
January 2023
Pages 52-64
  • Receive Date: 02 March 2022
  • Revise Date: 31 May 2022
  • Accept Date: 06 June 2022
  • First Publish Date: 08 June 2022