scholarly journals Elementary Quadrature for the Riccati equation

2020 ◽  
Keyword(s):  
Riccati Equation ◽  
Elementary Quadrature

Abstract The authors have requested that this preprint be withdrawn due to a need to make corrections.

scholarly journals Elementary Quadrature for the Riccati equation

2020 ◽  
Author(s):  
Ji-Xiang Zhao
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Analytical Method ◽  
Nonlinear Differential Equations ◽  
Integrability Condition ◽  
Type Equation ◽  
Abel Equation ◽  
General Solutions ◽  
Suitable Transformation ◽  
Elementary Quadrature

Abstract Using suitable transformation in combination with a specific Riccati-type equation solvable, the problem of solving Riccati equation can be transformed into that of a quasi-Abel equation of the second kind. By the extended Julia’s integrability condition, the general solutions of Riccati equation in the form of elementary quadrature are obtained, which contains numerous. This method opens up a new prospect for the study of nonlinear differential equations by analytical method.

scholarly journals The Riccati Equation and the Hidden Parameter &Variable

2021 ◽  
Author(s):  
Ji-Xiang Zhao
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Riccati Equation ◽  
Stokes Equation ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Elementary Quadrature ◽  
Linear Odes ◽  
Hidden Parameter

Abstract Using suitable function transformation in combination with a specific Riccati-type equation solvable, general solution of the Riccati equation in the form of elementary quadrature is given. In the process of solving the Riccati equation, the hidden parameter and variable are discovered. This indicates that hidden parameter & variable exist in all differential equations associated with the Riccati equation, such as the second-order linear ODEs, the Schrödinger equation and the Navier–Stokes equation.

On the solution of the Riccati equation by the Taylor matrix method

2006 ◽  
Vol 176 (2) ◽  
pp. 414-421 ◽  
Author(s):  
Mustafa Gülsu ◽  
Mehmet Sezer
Keyword(s):  
Riccati Equation ◽  
Matrix Method
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