Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Series Solution of High Order Abel, Bernoulli, Chini and Riccati Equations

  • Henk, Koppelaar (Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology) ;
  • Peyman, Nasehpour (Department of Engineering Science, Golpayegan University of Technology)
  • Received : 2021.06.17
  • Accepted : 2022.05.31
  • Published : 2022.12.31
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Abstract

To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form y' = ayn + by + c, n > 1, with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.

Keywords

Acknowledgement

The second author is supported by the Department of Engineering Science at the Golpayegan University of Technology and his special thanks go to the Department for providing all necessary facilities available to him for successfully conducting this research.

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