The Riccati Equation, Differential Transform, Rational Solutions and Applications  

作　　者：Malick Ndiaye Malick Ndiaye(Department of Mathematics and Computer Sciences, Marist College, Poughkeepsie, NY, USA)

机构地区：[1]Department of Mathematics and Computer Sciences, Marist College, Poughkeepsie, NY, USA

出　　处：《Applied Mathematics》2022年第9期774-792,共19页应用数学（英文）

摘　　要：In this article, the Riccati Equation is considered. Various techniques of finding analytical solutions are explored. Those techniques consist mainly of making a change of variable or the use of Differential Transform. It is shown that the nonconstant rational functions whose numerator and denominator are of degree 1, cannot be solutions to the Riccati equation. Two applications of the Riccati equation are discussed. The first one deals with Quantum Mechanics and the second one deal with Physics.In this article, the Riccati Equation is considered. Various techniques of finding analytical solutions are explored. Those techniques consist mainly of making a change of variable or the use of Differential Transform. It is shown that the nonconstant rational functions whose numerator and denominator are of degree 1, cannot be solutions to the Riccati equation. Two applications of the Riccati equation are discussed. The first one deals with Quantum Mechanics and the second one deal with Physics.

关 键 词：Riccati Equation Differential Transform Rational Solutions 

分 类 号：O175[理学—数学]