In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

We establish a new straightforward interpolation method for solving linear Volterra integral ‎‎equations with weakly singular kernels. The proposed is fundamentally different from all other published methods this type of equations. have modified some vector-matrix barycentric Lagrange formulas to be convenient interpolating the kernel twice concerning two variables and introducing ideas selecti...