Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph

P C Jayaprakasha; H C Shashikumar

doi:10.17485/IJST/v16i15.2353

Article

Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i15.2353

Year: 2023, Volume: 16, Issue: 15, Pages: 1159-1167

Original Article

Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph

P C Jayaprakasha^1*, H C Shashikumar²

¹Mathematics, Government First Grade College for Women, Tumkur, Karnataka, India
²Mathematics, Government Science College, Hassan, Karnataka, India

*Corresponding Author
Email: j[email protected]

Received Date:22 December 2020, Accepted Date:30 March 2023, Published Date:21 April 2023

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

Abstract

Objectives: Introduction to new numerical techniques to solve differential, difference, and integro-differential equations (IDEs) are always remaining the thrust area of research for many scientists over the centuries. The prime objective of this work is to contribute a new numerical technique to solve IDEs. Method: To address non-linear integro-differential equations, we computed an operational matrix of derivatives based on the Hosoya polynomial of the path graph in this work. Findings: Using the derived operational matrix, we have solved both Volterra and Fredholm integrodifferential equations. Taking suitable examples accuracy of the projected method is demonstrated in this paper in terms of a graphical representation of the absolute error. The results of the examples reveal that the projected method is a suitable method to solve IDEs. Novelty: The application of the Hosoya polynomial of path graph to solve integro-differential equations is a novel approach in the field of numerical analysis. Keywords: Volterra Integrodifferential equations; Fredhlom Integrodifferential equations; Graph theorypolynomials

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Copyright

© 2023 Jayaprakasha & Shashikumar. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)