On even-degree splines with application to quadratures

Tarazi, M. N. El; Karaballi, A. A.

doi:10.1016/0021-9045(90)90080-a

Cited by 8 publications

(8 citation statements)

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“…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).…”

Section: Illustrationsmentioning

confidence: 60%

“…The inequality (6) provides a correction of inequalities (5), (10), (15.4), (20), and (25) in El Tarazi and Karaballi (1990). …”

Section: Error Boundsmentioning

confidence: 99%

“…Consider the following Logarithmic Function (El Tarazi and Karaballi 1990; Rathod et al. 2010):The numerical solutions using twelfth degree spline are represented in Table 1, in case of .…”

Section: Illustrationsmentioning

confidence: 99%

“…2010):The numerical solutions using twelfth degree spline are represented in Table 1, in case of . In Table 2, maximum errors are reported corresponding to the present spline method and the spline method in El Tarazi and Karaballi (1990) for various values of h . Tables 3 and 4 show the comparison of the proposed spline method with the standard cubic splines (natural, clamped and a not a knot) and Subbotin cubic spline method developed in Rathod et al.…”

Section: Illustrationsmentioning

confidence: 99%

“…El Tarazi and Karaballi (1990) have constructed five types of even degree splines () that match the derivatives up to the order k at the knots of a uniform partition for each , and 5. These splines are also applied to quadrature.…”

Section: Introductionmentioning

confidence: 99%

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Twelfth degree spline with application to quadrature

Mohammed

Hamasalh

2016

SpringerPlus

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In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applicability and efficiency of the new method.

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“…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).…”

Section: Illustrationsmentioning

confidence: 60%

“…The inequality (6) provides a correction of inequalities (5), (10), (15.4), (20), and (25) in El Tarazi and Karaballi (1990). …”

Section: Error Boundsmentioning

confidence: 99%

“…Consider the following Logarithmic Function (El Tarazi and Karaballi 1990; Rathod et al. 2010):The numerical solutions using twelfth degree spline are represented in Table 1, in case of .…”

Section: Illustrationsmentioning

confidence: 99%

Section: Illustrationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations