Numerical Solution of Volterra's Integral Equation Using Runge-Kutta Methods (Second Order–Fourth Order)

Abstract

This scientific paper addresses the study of numerical solutions for Volterra integral equations using second-order and fourth-order Runge-Kutta methods. These equations appear in various fields such as physics, engineering, chemistry, and medical sciences, where it is difficult to obtain analytical and accurate solutions. The Volterra integral equation is transformed into a first-order or second-order differential equation depending on the nature of the equation, after which the Runge-Kutta method is applied. The results show that the use of the Runge-Kutta method provides accurate numerical solutions for Volterra integral equations. Numerical solutions using Runge-Kutta of different orders were compared, and it was clear that the numerical solution using the fourth-order Runge-Kutta method is more accurate than that using the second-order Runge-Kutta method, with results presented using MATLAB software. The study demonstrates that the Runge-Kutta method is an effective tool for solving Volterra integral equations.