286 citations · 587 across the 20 of their papers we have counts for
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Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains
Christian B. Mendl, Folkmar Bornemann
This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combin…
Numerical Methods for the Discrete Map
Folkmar Bornemann, Alexander Its, Sheehan Olver +1
As a basic example in nonlinear theories of discrete complex analysis, we explore various numerical methods for the accurate evaluation of the discrete map introduced by Agaf…
Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlevé II Transcendents
Georg Wechslberger, Folkmar Bornemann
The stability and convergence rate of Olver's collocation method for the numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very sensitively on the particular…
On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity
Shuhuang Xiang, Folkmar Bornemann
We study the optimal general rate of convergence of the n-point quadrature rules of Gauss and Clenshaw-Curtis when applied to functions of limited regularity: if the Chebyshev coef…
Optimal Contours for High-Order Derivatives
Folkmar Bornemann, Georg Wechslberger
As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bo…
On the Numerical Evaluation of Fredholm Determinants
Folkmar Bornemann
Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution funct…
A Model for Understanding Numerical Stability
Folkmar Bornemann
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is relat…
Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle
Folkmar Bornemann, Christian Rasch
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplifi…
Runge-Kutta methods, trees, and Mathematica
Folkmar Bornemann
A simple and elementary proof of Butcher's theorem on the order conditions of Runge-Kutta methods is presented. It is based on a recursive definition of rooted trees and avoids com…