scholarly journals Derivation of the errors involved in interpolation and their application to numerical quadrature formulae

1998 ◽  
Vol 92 (1) ◽  
pp. 59-68 ◽  
Author(s):  
A. Chakrabarti ◽  
Hamsapriye
Keyword(s):  
Numerical Quadrature ◽  
Quadrature Formulae

Numerical quadrature for Bessel transformations

2008 ◽  
Vol 58 (9) ◽  
pp. 1247-1261 ◽  
Author(s):  
Shuhuang Xiang ◽  
Weihua Gui ◽  
Pinghua Mo
Keyword(s):  
Numerical Quadrature

Developed Plate Expansion Using Geodesics

1984 ◽  
Vol 21 (04) ◽  
pp. 384-388
Author(s):  
John C. Clements
Keyword(s):  
Differential Equation ◽  
Numerical Quadrature ◽  
Developable Surface ◽  
Accuracy Control ◽  
Isometric Mapping ◽  
Variable Stepsize ◽  
Mapping Algorithm ◽  
Equation Solving ◽  
Expansion Procedure ◽  
The Relationship

This work is concerned with the application of a new isometric mapping algorithm to hull plate expansion procedures for ships with all or portions of the hull consisting of developable surfaces. The expansion procedure is based on the relationship between the ruling lines r⇀(s) generating the developable surface S⇀(s,t) and one additional geodesic g⇀(s) constructed within the surface as the solution of the differential equation det(g⇀'g⇀"n⇀) = 0 where n⇀ is the unit normal to S⇀ at g⇀. Precise accuracy control is achieved through the use of adaptive numerical quadrature and a variable stepsize differential equation solving routine.

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