The aims of this Julia package are: to be the fastest general purpose quadrature package, supporting the canonical interval, and semi-infinite and infinite domains in arithmetic up to and including BigFloat; and, to provide support for maximizing convergence rates when complex singularities are present near the contour of integration. Since the package can handle integrable algebraic and logarithmic endpoint singularities, and since it allows the user to consider other domains by declaring a new instance of the type Domain, the package is general purpose. The primary function of this module computes the nodes and weights of the trapezoidal rule, dot(f(x),w), after a variable transformation induces double exponential endpoint decay. In addition, the variable transformations maximize the convergence rate despite complex singularities near the solution interval. The secondary function of this module computes the parameters of the conformal map h(t) in Eq. (3.14) of . This module requires the use of the Julia package Ipopt for solving the nonlinear program.
References in zbMATH (referenced in 1 article )
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- Slevinsky, Richard Mikael; Olver, Sheehan: On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and sinc numerical methods (2015)