Numerical integration of logarithmic and nearly logarithmic singularity in BEMs
نویسندگان
چکیده
منابع مشابه
Evaluation of an Integral Arising in Numerical Integration Near a Logarithmic Singularity
the two forms for / converge or diverge together. Equation (4) follows from (2) by partial integration. Now the integral in (3) can be approximated by any one of several standard methods. The approximate evaluation of (2) can therefore be achieved, once the evaluation of (1) is completed. In this note coefficients of the Lagrangian type are presented to facilitate the computation of /. A rigoro...
متن کاملEvaluation of an Integral Arising in Numerical Integration Near a Logarithmic Singularity
the two forms for / converge or diverge together. Equation (4) follows from (2) by partial integration. Now the integral in (3) can be approximated by any one of several standard methods. The approximate evaluation of (2) can therefore be achieved, once the evaluation of (1) is completed. In this note coefficients of the Lagrangian type are presented to facilitate the computation of /. A rigoro...
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Let fa,L : R→ R be such that (1) fa,L : θ 7→ θ + a + L ln |Φ(θ)| where a ∈ [0, 1], L ∈ R are real parameters and Φ(θ) is such that Φ(θ + 1) = Φ(θ). We assume that Φ(θ) is a Morse function and the graph of y = Φ(θ) is transversal to the θ-axis. The functions fa,L induce a two parameter family of 1D maps from S1 to S1 where S1 = R/Z is the unit circle. In this paper we prove that there exists an ...
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ژورنال
عنوان ژورنال: Applied Mathematical Modelling
سال: 2001
ISSN: 0307-904X
DOI: 10.1016/s0307-904x(01)00021-x