Triangular functions method for the solution of Fredholm integral equations system

A numerical method based on orthogonal triangular functions (TFs) is proposed to approximate the solution of Fredholm integral equations systems. The powerful properties of orthogonal triangular functions are utilized in a direct method to reduce a system of Fredholm integral equations to a system of mere algebraic equations. The proposed method does not need any integration for obtaining the constant coefficients hence, it can be applied in a simple and fast technique. Convergence analysis and associated theorems are considered. Some numerical examples illustrate the accuracy and computational efficiency of the proposed method.