On RHF and Bernoulli Polynomial for the numerical solution of differential equations

Khan, Anjum; Reshamwale, Basit Ali; Hegde, Sharan; Shetty, Sowmya Ashwin

doi:10.36647/ijsem/09.03.a007

Cited by 1 publication

(1 citation statement)

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“…To determine the analytical solution to the linear and nonlinear FIDE and VIDE, A. S. Khan (3) has used a variation of parameter techniques. Numerous academics have recently worked on integro-differential equations and achieved superior results (4)(5)(6)(7)(8)(9)(10)(11) . The study of integral and IDEs, which contain two different types of integral operators, was the main emphasis of Hamoud and Ghadle (12) .…”

Section: Introductionmentioning

confidence: 99%

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

Jayaprakasha¹,

Shashikumar²

2023

IJST

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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.

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