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Numerical Methods to Solve Fractional Order Optimal Control Problems. Numerical Simulation of Fractional HIV Models Using Some Numerical Methods
В наличии
Местонахождение: Алматы | Состояние экземпляра: новый |
Бумажная
версия
версия
Автор: Yousef S. Almaghrebi,Nasser Sweilam and Abdelhameed Nagy
ISBN: 9783330040267
Год издания: 2017
Формат книги: 60×90/16 (145×215 мм)
Количество страниц: 124
Издательство: LAP LAMBERT Academic Publishing
Цена: 30322 тг
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Аннотация: In this book, two existing mathematical models to describe the human immunodeficiency virus (HIV) disease are studied. The adopted models are described by a system of nonlinear ordinary differential equations (ODEs). Optimal control for HIV models is presented. The Pontryagin's Maximum Principle (PMP) is used to derive the optimality system (OS) which is solved numerically using the nonstandard finite difference method (NSFDM), standard finite difference method (SFDM) and forward-backward sweep method (FBSM). Existences and uniqueness for the solutions of the mathematical models are proved. Also, two general HIV models are presented as fractional-order mathematical models. The fractional derivative is defined in the sense of Caputo definition. The shifted Chebyshev spectral method (SCSM) is used to study the OS for the first model. Two different numerical methods are introduced to study the optimal control problems of both models. These methods are iterative optimal control method (IOCM) and the generalized Euler method (GEM).
Ключевые слова: fractional calculus, optimal control theory, Mathematical model of HIV, Nonstandard finite difference, Shifted Chebyshev spectral method, Generalized Euler method
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