In this study, an alternative numerical method having regard to the Bernstein operator is generated for approximate solutions of linear differential equations in most general form under initial and boundary conditions. Some applications are also revealed show how procedure can be performed problems.

It easy to see that every bounded linear operator is continuous. It is not hard to show that the converse is also true. The notions of bounded and continuous thereby coincide for linear operators acting between normed spaces. It is customary to prefer the terminology bounded linear operator over that of continuous linear operator. The reason for this preference is the fact that the hard part of...