Analytical Approach to Solving Volterra Integral Equations using the Adomian Decomposition Method

E. Ashok Lakshmana Rao

Abstract: This paper explores the application of the Adomian Decomposition Method ADM in providing numerical solutions to Volterra Integral Equations. The ADM, a powerful tool for solving nonlinear equations, is presented as an efficient method that approximates the solution as an infinite series, converging to the exact solution. The paper demonstrates the efficacy and precision of the ADM through several numerical examples, highlighting its potential in solving first, second, and third order differential and integral equations. The study underscores the versatility of the ADM in solving linear and nonlinear problems across various fields such as Mathematics, Physics, Biology, and Chemistry.

Keywords: Adomian Decomposition Method, Integral Equations, Volterra Integral Equations, Numerical Example