Bernstein operator method for approximate solution of singularly perturbed Volterra integral equations

Abstract An approximate solution of integral equations takes an active role in the numerical analysis. This paper presents and tests an algorithm for the approximate solution of singularly perturbed Volterra integral equations via the Bernstein approximation technique. The method of computing the numerical approximation of the solution is properly demonstrated and exemplified in the matrix notation. Besides, the error bound and convergence associated with the numerical scheme are constituted. Finally, particular examples indicate the dependability and numerical capability of the introduced scheme in comparison with other numerical techniques.