Numerical Simulation of Initial Value Problem of Integro-differential Equation Models

Authors

  • Faizah Alharbi Umm Al-Quraa University
  • Sharifah Althubiti Umm Al-Quraa University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.5024

Keywords:

integro-differential equations (IDE), Volterra-Friedholm integral equation (V-FIE), system of second-order Fredholm integral equations (SFIEs), collocation Method and Galerkin method.

Abstract

In this article, the Volterra-Fredholm integral equation (V-FIE) is derived from an initial value problem of kind integro-differential equation (IVP). We discuss the existence and uniqueness of the solution to the problem in Hilbert space. A numerical method is used to reduce this type of equation to System of Fredholm integral equations of the second kind(SFIEs). In light of this, the clustering method and the Galerkin method to solve the system of second-order Fredholm integral equations(SFIEs) and calculate the error in each case. Finally, the approximate and exact solutions are plotted on the same coordinate plane Using MATLAB code (2022).

Author Biography

  • Sharifah Althubiti, Umm Al-Quraa University

    Mathematices Department, Faculty of Sciences 

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Published

2024-01-31

Issue

Vol. 17 No. 1: (January 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 European Journal of Pure and Applied Mathematics

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How to Cite

Numerical Simulation of Initial Value Problem of Integro-differential Equation Models. (2024). European Journal of Pure and Applied Mathematics, 17(1), 286-299. https://doi.org/10.29020/nybg.ejpam.v17i1.5024