Riccati equation, a new analytical method for solving Riccati equation and engineering applications


Thesis Type: Postgraduate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2017

Thesis Language: Turkish

Student: Mutlu Özgür Ertaş

Supervisor: YAŞAR PALA

Abstract:

The Riccati equation emerges in various forms in many disciplines where mathematical models are made. It can be talked about a wide range of applications such as control systems, programming of automatic systems, financial models, quantum mechanics, mathematical modeling of many physical states. The Riccati equation can be reached by means of direct-side transformation methods for solving problems, which are usually called non-linear, problems involving behavioral systems. It has been one of the main topics of mathematical science because of the fact that until now a certain analytical solution method cannot be found in every circumstance appropriately. The solution methods that have been tried to be developed so far are only analytically operating under certain conditions, and can provide some solutions with numerical approaches. In this study, we will examine the existing solution methods which are known, then we will try to reinforce it with examples by developing a new solution method and finally we will solve the problems that are encountered in practical applications with this new method. The new method presented easily demonstrates that a given Riccati equation, attempted to be solved, has an analytical solution with a simple transformation included. Studies on the Riccati equation, a first-order nonlinear differential equation, are still in progress. In the world of science, various books have been written in many subjects related to the Riccati equation, many articles have been published and are still being written / published.