On the numerical integration of certain singular integrals

Computing ◽  
1992 ◽  
Vol 48 (2) ◽  
pp. 177-189 ◽  
Author(s):  
H. W. Stolle ◽  
R. Strauss
Keyword(s):  
Numerical Integration ◽  
Singular Integrals

Numerical integration schemes for evaluation of (hyper)singular integrals in 2D BEM

1998 ◽  
Vol 22 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A. Aimi ◽  
A. Carini ◽  
M. Diligenti ◽  
G. Monegato
Keyword(s):  
Numerical Integration ◽  
Singular Integrals ◽  
Integration Schemes

scholarly journals Analysis of Numerical Measure and Numerical Integration Based on Measure

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yinkun Wang ◽  
Jianshu Luo ◽  
Xiangling Chen
Keyword(s):  
Numerical Method ◽  
Convergence Analysis ◽  
Numerical Integration ◽  
Error Bound ◽  
Lagrange Interpolation ◽  
Singular Integrals ◽  
Specific Method ◽  
Numerical Examples ◽  
Measure Function ◽  
Theoretical Results

We present a convergence analysis for a general numerical method to estimate measure function. By combining Lagrange interpolation, we propose a specific method for approximating the measure function and analyze the convergence order. Further, we analyze the error bound of numerical measure integration and prove that the numerical measure integration can decrease the singularity for singular integrals. Numerical examples are presented to confirm the theoretical results.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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