<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted strategy, the desired outcome is expanded in the form of a collection of continuous polynomials over an interval. Nevertheless, compared to other methods for solving differential equations, this method’s precision and effectiveness relies on the size of the collection of Hosoya polynomials, and the process is easier. Excellent agreement between the exact and approximate solutions is obtained when the current scheme is used to crack linear and nonlinear equations. Potentially, this method could be used in more intricate systems for which there are no exact solutions.</p>
</abstract>

We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted strategy, the desired outcome is expanded in the form of a collection of continuous polynomials over an interval. Nevertheless, compared to other methods for solving differential equations, this method’s precision and effectiveness relies on the size of the collection of Hosoya polynomials, and the process is easier. Excellent agreement between the exact and approximate solutions is obtained when the current scheme is used to crack linear and nonlinear equations. Potentially, this method could be used in more intricate systems for which there are no exact solutions.

Solutions of differential equations using linearly independent Hosoya polynomials of trees

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted...

Solutions of differential equations using linearly independent Hosoya polynomials of trees

Article Category: Original Study

Published Online: Oct 31, 2023

Page range: 13 - 22

Received: Jun 06, 2023

Accepted: Jul 22, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0002

Keywords
Differential equations, Lane-Emden equation, Hosoya polynomial, numerical solution

© 2024 Kumbinarasaiah Srinivasa et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Solutions of differential equations using linearly independent Hosoya polynomials of trees

Article Category: Original Study

Published Online: Oct 31, 2023

Page range: 13 - 22

Received: Jun 06, 2023

Accepted: Jul 22, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0002

KeywordsDifferential equations, Lane-Emden equation, Hosoya polynomial, numerical solution

© 2024 Kumbinarasaiah Srinivasa et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Differential equations, Lane-Emden equation, Hosoya polynomial, numerical solution