Acceleration of Gauss-legendre Quadrature for an Integrand with an Endpoint Singularity
نویسنده
چکیده
An asymptotic error expansion for Gauss-Legendre quadrature is derived for an integrand with an endpoint singularity. It permits convergence acceleration by extrapolation.
منابع مشابه
Variable transformations and Gauss-Legendre quadrature for integrals with endpoint singularities
Gauss–Legendre quadrature formulas have excellent convergence properties when applied to integrals ∫ 1 0 f(x) dx with f ∈ C∞[0, 1]. However, their performance deteriorates when the integrands f(x) are in C∞(0, 1) but are singular at x = 0 and/or x = 1. One way of improving the performance of Gauss–Legendre quadrature in such cases is by combining it with a suitable variable transformation such ...
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