Bernstein approximation technique for numerical solution of Volterra integral equations of the third kind

We propose a numerical scheme based upon the Bernstein approximation method for computational solution of a new class of Volterra integral equations of the third kind (3rdVIEs). Construction of the technique and its practicality for proposed equations have been introduced. Furthermore we have examined the numerability and convergence analysis of the proposed scheme. Finally, we demonstrate a series of numerical examples demonstrating the effectiveness of this new technique for solving 3rdVIEs.

Automated summary

This study presents a numerical scheme based on the Bernstein approximation method for solving a new class of Volterra integral equations of the third kind. It introduces the construction of the technique, its practicality, numerability, and convergence analysis, along with demonstrating the effectiveness through a series of numerical examples.