Shifted Chebyshev polynomials for Solving Three-Dimensional Volterra Integral Equations of the second kind

TL;DR

This paper introduces a numerical method using shifted Chebyshev polynomials to efficiently solve three-dimensional Volterra integral equations of the second kind, transforming them into algebraic equations for easier computation.

Contribution

The paper presents a novel application of shifted Chebyshev polynomials to solve 3D Volterra integral equations, providing an effective computational approach.

Findings

Numerical results demonstrate high accuracy of the method.

The approach effectively reduces integral equations to algebraic form.

Estimated errors are computed and show the method's reliability.

Abstract

In this paper, an efficient method is presented for solving three dimensional Volterra integral equations of the second kind with continuous kernel. Shifted Chebyshev polynomial is applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. Numerical results are calculated and the estimated error in each example is computed using Maple 17.