Triangular functions in solving Weakly Singular Volterra integral equations

Abstract

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.