Triangular functions method for the solution of Fredholm integral equations system

AbstractA 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