Numerical Simulation of Initial Value Problem of Integro-differential Equation Models
Keywords:integro-differential equations (IDE), Volterra-Friedholm integral equation (V-FIE), system of second-order Fredholm integral equations (SFIEs), collocation Method and Galerkin method.
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).
Copyright (c) 2024 European Journal of Pure and Applied Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.