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POLAT, GÜLDEN GÜN

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Dr. Öğr. Üyesi

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POLAT

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GÜLDEN GÜN

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2020 - 20212
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Subject: Lie Point Symmetries

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Now showing 1 - 2 of 2
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    On Group Analysis of Optimal Control Problems in Economic Growth Models
    (American Institute of Mathematical Sciences, 2020) POLAT, GÜLDEN GÜN; Özer, Teoman
    The optimal control problems in economic growth theory are analyzed by considering the Pontryagin's maximum principle for both current and present value Hamiltonian functions based on the theory of Lie groups. As a result of these necessary conditions, two coupled first-order differential equations are obtained for two different economic growth models. The first integrals and the analytical solutions (closed-form solutions) of two different economic growth models are analyzed via the group theory including Lie point symmetries, Jacobi last multiplier, Prelle-Singer method,_-symmetry and the mathematical relations among them.
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    On Ramsey Dynamical Model and Closed-Form Solutions
    (Springer Nature, 2021) POLAT, GÜLDEN GÜN; Özer, Teoman
    This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions of maximum principle are analyzed and then first integrals and corresponding closed-form (analytical) solutions are determined by using Lie point symmetries in conjunction with Prelle-Singer and Jacobi last multiplier methods. Additionally, associated lambda-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.