One point quadrature rule with cardinal B-spline

Abstract

To compute approximately an integral (1) ∫ 0 m φ m ( x ) f ( x ) d x , where φ m ( ⋅ ) is cardinal B-spline, we used composite rectangular rule. We proved that, on the “quasi uniform” mesh, the used formula has, conditionally speaking, algebraic degree of exactness m − 1 . Under additional assumptions, algebraic degree of exactness is m .