Solving Two –Dimensional Volterra Integral Equation Using the Double Laplace Transform

Abstract

This study investigates an efficient analytical approach for solving two-dimensional Volterra integral equations by employing the double Laplace transform technique. To establish a solid mathematical foundation, we first review the essential definitions, core concepts, and fundamental theoretical properties governing the double Laplace transform. Particular emphasis is placed on the convolution theorem and its practical implications, alongside a rigorous discussion on the existence and uniqueness of the solution. To demonstrate the validity and effectiveness of the discussed framework, the method is successfully implemented to resolve specific instances of Volterra integral equations, showcasing its accuracy and computational reliability.