On the numerical solution of Volterra integral equations on equispaced nodes

TL;DR

This paper introduces a Nystrom-type numerical method using generalized Bernstein polynomials for solving second kind Volterra integral equations on equispaced nodes, with analysis of stability, convergence, and numerical performance.

Contribution

The paper presents a novel Nystrom-type method based on generalized Bernstein polynomials for second kind Volterra equations, focusing on equispaced nodes.

Findings

Method demonstrates stability and convergence in continuous function space.

Numerical tests confirm the effectiveness of the proposed approach.

Approach performs well on test problems with accurate solutions.

Abstract

In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced points. Stability and convergence are studied in the space of continuous functions, and some numerical tests illustrate the performance of the proposed approach.