On approximate solutions of a class of Clairaut’s equations
作者：
Highlights：
• This is the first study on the Ulam type stability of Clairaut’s equation. Based on the behavior of the solutions of a class of Clairaut’s equations, the error (magnitude) of the approximate and exact solutions is explicitly shown.
• In addition, this study provided important ideas for analyzing the solutions of differential equations which have non-unique solutions.
• To understand the obtained results, examples are provided with numerical simulations.
摘要
•This is the first study on the Ulam type stability of Clairaut’s equation. Based on the behavior of the solutions of a class of Clairaut’s equations, the error (magnitude) of the approximate and exact solutions is explicitly shown.•In addition, this study provided important ideas for analyzing the solutions of differential equations which have non-unique solutions.•To understand the obtained results, examples are provided with numerical simulations.
论文关键词：Approximate solution,Perturbation,Clairaut’s equation,Nonlinear differential equation,Ulam stability
论文评审过程：Received 9 March 2022, Revised 19 April 2022, Accepted 23 April 2022, Available online 13 May 2022, Version of Record 13 May 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127205
