A new computational method based on the Picard iteration method for solving boundary optimal control problems governed by PDEs with two-point boundary conditions

Karim Benalia; Karim Beddek; Thiziri Sifaoui; Brahim Oukacha

doi:10.24193/subbmath.2026.1.11

Authors

Karim Benalia Department of Mathematical Sciences, Faculty of Hydrocarbons and Chemistry, University of Boumerdes, Algeria https://orcid.org/0000-0002-0445-8559
Karim Beddek M'Hamed Bougara University of Boumerdes, Algeria https://orcid.org/0000-0003-2184-9399
Thiziri Sifaoui Department of Mathematics and Computer Science, Faculty of Sciences and Technology, University of Amine Elokkal El Hadj Moussa Eg akhamouk, Tamanghasset, Algeria https://orcid.org/0009-0007-6884-0611
Brahim Oukacha Department of Mathematics, University of Tizi Ouzou, Algeria https://orcid.org/0009-0006-5172-6356

DOI:

https://doi.org/10.24193/subbmath.2026.1.11

Keywords:

optimal control problem, Picard iteration method, Pontryagin's minimum principle

Abstract

This paper presents a new computational method based on the Picard iteration method for solving boundary optimal control problems governed by parabolic partial differential equations with two-point boundary conditions. The proposed approach adapts the Picard iteration method to solve the necessary optimality conditions derived from Pontryagin’s minimum principle, yielding a solution expressed as a truncated power series. To evaluate the effectiveness of the proposed method, a numerical example is provided, and the obtained results are compared with those derived from an alternative approach, demonstrating the accuracy and reliability of the method.

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