Triangular functions in solving Weakly Singular Volterra integral equations

In this paper, we propose the triangular orthogonal functions as a basis functions for solution of weakly singular Volterra integral equations of the second kind. Powerful properties of these functions and some operational matrices are utilized in a direct method to reduce singular integral equation to some algebraic equations. The presented method does not need any integration for obtaining the constant coefficients. The method is computationally attractive, and applications are demonstrated through illustrative examples.