On approximate solutions of a class of Clairaut’s equations

Masakazu Onitsuka and Iz-iddine El-Fassi

Applied Mathematics and Computation, 2022, vol. 428, issue C

Abstract: It is well known that Clairaut’s equation can be solved, but its perturbed equation cannot. In addition, Clairaut’s equation has two interesting properties: it has a singular solution and no uniqueness of the solutions. This study overcomes these difficulties and analyzes the error between the approximate and exact solutions of Clairaut’s equation. Moreover, it contains important ideas as an approach to differential equations which have non-unique solutions. Examples and numerical simulations are given to understand the results.

Keywords: Approximate solution; Perturbation; Clairaut’s equation; Nonlinear differential equation; Ulam stability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:428:y:2022:i:c:s009630032200279x

DOI: 10.1016/j.amc.2022.127205

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