Numerical solution of the biharmonic equation using different types of bivariate spline functions

AbstractThe paper gives details of a case study in the premium rating of a Householders Contents insurance portfolio. The rating is performed by the fitting of bivariate spline functions to a version of operating ratio described in Section 3.The use of bivariate splines requires a small amount of mathematical equipment, which is developed in Section 4. The fitting of splines, using regression is carried out in Sections 5 and 6, where the numerical results are given, including some assessment of goodness-of-fit.Contour maps of the spline surfaces are also given, and used for the selection of geographic areas used for premium rating purposes. These are compared with the areas, past and present, actually used by the insurer concerned.

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Fifth order of non-polynomial spline functions to find a second type integral numerical solution linear Volterra with weakly singular kernel

Journal of Physics Conference Series ◽

10.1088/1742-6596/1892/1/012022 ◽

2021 ◽

Vol 1892 (1) ◽

pp. 012022

Author(s):

Ahmed Sh. Hamad

Keyword(s):

Numerical Solution ◽

Polynomial Spline ◽

Singular Kernel ◽

Spline Functions ◽

Weakly Singular Kernel ◽

Weakly Singular ◽

Type Integral ◽

Fifth Order

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Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Archives of Hydro-Engineering and Environmental Mechanics ◽

10.1515/heem-2015-0022 ◽

2015 ◽

Vol 62 (3-4) ◽

pp. 101-119 ◽

Cited By ~ 1

Author(s):

Wojciech Artichowicz ◽

Dzmitry Prybytak

Keyword(s):

Numerical Methods ◽

Numerical Solution ◽

Numerical Integration ◽

Cross Sections ◽

Flow Model ◽

One Dimensional ◽

Averaging Methods ◽

Integration Formulas ◽

Different Types ◽

The One

AbstractIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

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