F-transform utility in the operational-matrix approach to the Volterra integral equation

The proposed approach, based on the F-transform, consists in constructing an operational matrix for the Volterra integral equation as a Hadamard product of two matrices, one of which refers to the Volterra operator, and the other to its kernel. As a result, the F-transformed form of the entire equation reduces to a system of linear equations with a triangular matrix. This makes the corresponding numerical method for solving the Volterra integral equation efficient and low computational. We provide all the necessary proofs of the supporting statements, including the convergence of the method, and estimate its computational complexity. Finally, we illustrate the proposed algorithm with test cases and compare their results with some recently published methods.