Chebyshev series solutions of Fredholm integral equations

Abstract

A matrix method for approximately solving certain linear and non‐linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Chebyshev series approximation. The method is based on first taking the truncated Chebyshev series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear or non‐linear system of algebraic equations with unknown Chebyshev coefficients. In addition, some equations considered by other authors are solved in terms of Chebyshev polynomials and the results are compared.