2020/07/28 by Joren Vanherck, Vanherck, Joren, Bart Sorée +3 · 1 citation
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Geophysics and Gravity Measurements #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2007.15057
openalex publication_date 2020/07/28 · openalex created_date 2020/08/03 · openalex updated_date 2026/07/28
The problem of estimating single- and multi-dimensional integrals, with or without end-point singularities, is prevalent in all fields of scientific research, and in particular in physics. Although tanh-sinh quadrature is known to handle most of these cases excellently, its use is not widely spread among physicists. Moreover, while most calculations are limited by the use of finite-precision floating-point arithmetic, similar considerations for tanh-sinh quadrature are mostly lacking in literature, where infinite-precision floating-point numbers are often assumed. Also little information is available on the application of tanh-sinh quadrature to multiple integration. We have investigated the risks and limitations associated with limited-precision floating-point numbers when using tanh-sinh quadrature for both single and multiple integration, while obtaining excellent convergence rates. In addition, this paper provides recommendations for a straightforward implementation using limited-precision floating-point numbers and for avoiding numerical instabilities.