Two-dimensional Chebyshev hybrid functions and their applications to integral equations

A combination of bivariate Chebyshev polynomials and two-dimensional block-pulse functions are introduced and applied for approximating the numerical solution of two-dimensional Fredholm integral equations. All calculations in this approach would be easily implemented. The method has the advantage of reducing computational burden. The convergence analysis is given. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the proposed method.