The use of approximate functions for the numerical solution of Laplace' equation by an integral equation

1979 ◽  
Vol 10 (4) ◽  
pp. 709-711
Author(s):  
G. De Mey
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Laplace Equation

Haar Wavelet for the Natural Boundary Integral Equation

2014 ◽  
Vol 635-637 ◽  
pp. 1569-1573
Author(s):  
Zhe Wang
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Explicit Expression ◽  
Boundary Integral Equation ◽  
Laplace Equation ◽  
Haar Wavelet ◽  
Boundary Integral ◽  
Natural Boundary ◽  
Wavelet Method ◽  
Numerical Example

In this paper, we construct Haar wavelet and apply it to investigate the numerical solution of the natural boundary integral equation of the Laplace equation in the concave angle domains. Haar wavelet has better stability and good explicit expression. Moreover, they are mutual orthogonal. We make full use of their mutual orthogonal to cope with the natural boundary integral equation. Taking advantage of Galerkin-wavelet method in discretizing the natural boundary integral equation. Finally, a numerical example is shown and the feasibility and validity of the method are proved.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

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