Using W Transform for Solving Volterra Integro-Differential Equations

Abstract

There are numerous uses for the Volterra integro-differential equation in the fields of mechanics, geometric probability, population dynamics, theory of rejuvenation, facts on particle size and the damping of string vibration, and transmission of heat issues. Finding the approximate or exact solutions to these equations is of interest to many mathematicians and scientists. Our aim of this paper is to explore and figure out the solution of the Volterra integro-differential equation with a convolution kernel. We now introduce the W transform for determining the solution of linear Volterra integro-differential equation of the second kind and their system. The ability of the W Transform to solve these equations is shown by real-world applications. Based on what we discovered, the W Transform is an effective method for locating precise answers to the linear Volterra integro-differential equation of the second kind and their system.