Chebyshev collocation treatment of Volterra-Fredholm integral equation with error analysis

摘要

This work reports a collocation algorithm for the numerical solution of a Volterra-Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss-Chebyshev nodes were then used to reduce the Volterra-Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.