Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals
- Elliott, D
- Johnston, PR
DOIAbstract
In the two-dimensional boundary element method, one often needs to evaluate numerically integrals of the form where j2 is a quadratic, g is a polynomial and f is a rational, logarithmic or algebraic function with a singularity at zero. The constants a and b are such that -1a1 and 0<b1 so that the singularities of f will be close to the interval of integration. In this case the direct application of Gauss–Legendre quadrature can give large truncation errors. By making the transformation x=a+bsinh(μu-η), where the constants μ and η are chosen so that the interval of integration is again [-1,1], it is found that the truncation errors arising, when the same Gauss–Legendre quadrature is applied to the transformed integral, are much reduced. The...
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