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International Journal of Mathematics and Mathematical Sciences, 1987 In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of ...
Lloyd K. Williams
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Exploring the exact solutions to the nonlinear systems with neural networks method [PDF]
Scientific ReportsThis paper explores the use of Riccati subequation neural networks to solve nonlinear partial differential equations modeling complex biological processes like cancer, brain function, and wound healing.
Jan Muhammad +3 more
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Mean--field control and Riccati equations
Networks and Heterogeneous Media, 2015 We present a control approach for large systems of interacting agents based on the Riccati equation. If the agent dynamics enjoys a strong symmetrythe arising high dimensional Riccati equation is simplified and the resulting coupled system allows for a ...
Michael Herty +2 more
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Solving of some nonlinear ordinary differential equations in the form of power series
Физико-химические аспекты изучения кластеров, наноструктур и наноматериалов, 2022 In the current scientific literature, a variety of nonlinear ordinary differential equations are widely and successfully used to describe real processes in various fields of natural sciences: optics, elasticity theory, molecular physics, etc. For example,
I.N. Belyaeva +2 more
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Numerical solution of nonlinear fractional Riccati differential equations using compact finite difference method [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 This paper aims to apply and investigate the compact finite difference methods for solving integer-order and fractional-order Riccati differential equations. The fractional derivative in the fractional case is described in the Caputo sense.
H. Porki, M. Arabameri, R. Gharechahi
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About one problem of optimal control synthesis [PDF]
E-Journal of Analysis and Applied Mathematics, 2023 This paper tackles the problem of characterizing the natural class, or Riccati rule space, of solutions to a specific e quation. Despite the significant theoretical and practical implications, there is limited research exploring the application of ...
Muhametberdy Rakhimov
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A Forgotten Differential Equation Studied by Jacopo Riccati Revisited in Terms of Lie Symmetries
Mathematics, 2021 In this paper we present a two parameter family of differential equations treated by Jacopo Riccati, which does not appear in any modern repertoires and we extend the original solution method to a four parameter family of equations, translating the ...
Daniele Ritelli
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Riccati transfer equations for fluid structure interaction in liquid-filled piping systems
Heliyon, 2023 In this paper, based on the Riccati transfer matrix method (RTMM), the Riccati fluid structure interaction transfer equations (FSIRTE) are established to improve the numerical stability of the classical fluid structure interaction transfer matrix method (
Li Tang +3 more
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Matematika, 2019 Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional.
Muhamad Deni Johansyah +4 more
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Approximate solution for quadratic Riccati differential equation
Journal of Taibah University for Science, 2017 The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science.
Fateme Ghomanjani, Esmaile Khorram
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