Utilizing the Upadhyaya Transform to solve the linear second kind Volterra Integral Equation

Abstract

Volterra integral equations have a wide range of applications in mechanics, linear visco-elasticity, renewal theory, particle size statistics, damped vibration of a string, heat transfer problems, geometric probability, population dynamics, and epidemic studies. Many mathematicians and scientists are interested in finding either approximate or exact solutions to these equations. Upadhyaya Transform (UT) will be used in this paper to solve linear second type V.I.E. To accomplish this, the linear second type V.I.E. kernel has adopted a convolution type kernel. Some numerical examples are taken into account in order to outline the entire process of arriving at the solution. According to our findings, the Upadhyaya Transform (UT) is a powerful tool for finding solutions to the Linear Second kind V.I.E.

An innovative iterative approach to solving Volterra integral equations of second kind

“…Solving these equations poses a challenge due to their nonlinearity and complex mathematical implications. Solving Volterra integral equations of the second kind requires specialised techniques, such as Laplace transformations, numerical analysis, and numerical approximation methods to obtain accurate and reliable results [9][10][11][12][13].…”