Direct cubic spline with application to quadrature

Abstract

SUMMARYThis paper presents a formulation of a cubic spline that fits the first derivatives of a function at mesh points and the function value and its second derivative at the beginning of the interval. Error bounds for the function and its first three derivatives are derived over the whole interval. This formulation can be applied, in particular, to quadratures.

Twelfth degree spline with application to quadrature

“…The results of our methods are better than those has lower order (Anwar and El-Tarazi 1989; El Tarazi and Karaballi 1990; Rathod et al. 2010).…”

“…(1967), El Tarazi and Karaballi (1990), Phythian and Williams (1986), where a different approach was used. Moreover, the performance of the proposed twelfth degree spline with the even degree splines (El Tarazi and Karaballi 1990), direct cubic spline (Anwar and El-Tarazi 1989), standard cubic splines (natural, clamped and a not a knot) and Subbotin cubic spline (Rathod et al. 2010; Rathod et al.…”

“…The maximum absolute errors are tabulated in Table 6 for various values of h and compared with Anwar and El-Tarazi (1989). Figure 2 illustrates the comparison of numerical solution and analytical solution values at .…”