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On approximate solutions of a class of Clairaut’s equations

Author

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  • Onitsuka, Masakazu
  • El-Fassi, Iz-iddine

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.

Suggested Citation

  • Onitsuka, Masakazu & El-Fassi, Iz-iddine, 2022. "On approximate solutions of a class of Clairaut’s equations," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s009630032200279x
    DOI: 10.1016/j.amc.2022.127205
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