Three-Dimensional Volterra Integral Equations of the Second Kind

In this paper, an efficient method is presented for solving three-dimensional Volterra integral equations of the second kind with a continuous kernel. The method utilizes shifted Chebyshev polynomials to approximate solutions to these integral equations. By transforming the integral equation into algebraic equations with unknown Chebyshev coefficients, this approach allows for effective numerical solutions. Numerical results demonstrate the efficacy of the method, with estimated errors computed for each example using Maple 17. This study provides a robust framework for addressing complex integral equations in three-dimensional spaces, contributing to advancements in mathematical analysis and computational techniques.