Conversion of Ordinary Differential Equation with Initial Condition (Initial Value Problem) into Volterra Integral Equation by Using Two Methods, Both the Methods Give Different and Perfect Volterra Integral Equation for Some Problems

Arun Joshi¹ , Anuj Joshi² , Ritu ³

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.5 , pp.76-82, Oct-2019

Online published on Oct 31, 2019

Copyright © Arun Joshi, Anuj Joshi, Ritu . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This is based on some of the ordinary differential equation with initial boundary condition problem or initial value problem solved by the two methods and converted the ordinary differential equation with initial boundary condition or initial value problem into Volterra integral equation. The solution of these ordinary differential equation with initial condition or initial value problem by using the two methods are different solution but the solutions are correct. In Both the methods it always convert the ordinary differential equation with initial boundary condition or initial value problem into volterra integral equation. We are applying the two different methods in some of the ordinary differential equation with initial boundary condition or initial value problem .Then solutions of some problems give different volterra integral equation and some problems give same volterra integral equation but all the solutions are correct and perfect because all the solutions are satisfied by the condition of volterra integral equation. This shows that both the methods are correct to convert the ordinary differential equation with initial boundary condition problem or initial value problem into volterra integral equation

Key-Words / Index Term :
Ordinary differential equation, Initial value problem, Initial boundary condition, Volterra integral equation, linear Volterra integral equation, linear Volterra integral equation of second kind

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