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Kyungpook Mathematical Journal 2022; 62(4): 729-736

Published online December 31, 2022

Copyright © Kyungpook Mathematical Journal.

Series Solution of High Order Abel, Bernoulli, Chini and Riccati Equations

Henk Koppelaar∗, Peyman Nasehpour

Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands
e-mail : Koppelaar.Henk@gmail.com

Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran
e-mail : nasehpour@gut.ac.ir and nasehpour@gmail.com

Received: June 17, 2021; Revised: May 13, 2022; Accepted: May 31, 2022

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: Abel equation, Bernoulli equation, Chini equation, JCPMiller algorithm, Riccati equation, series solution