Analytical and numerical treatment of the Volterra equation of the second kind.

This paper presents the study of numerical solutions to the linear integral Volterra equation of the second type because of this type of equations of great importance in several fields, including the science of population structures as well as in the study of physical problems and concepts such as elasticity. It is also used in mathematics in the study of probability theory, differential calculation and integration of equations, approximation problems, and boundary conditions. Two methods of numerical solution were used, which is the Adomian publication method, as this method leads to accurate calculations and approximate solutions of differential equations easily, as a solution to the Volterra equation of the second type was reached without the need for large calculations or any other transformations. The second method is the Taylor series, where we were able to find approximate solutions to the Volterra equation of the second type, as Taylor approximation is of great importance in numerical mathematics and the algorithms adopted to solve the equations. It was the use of the program Mathematica to draw the results that have been reached. [ABSTRACT FROM AUTHOR]