3 papers
math.CA2026
The Lagrange Inversion Theorem with Limited Smoothness
J. Thomas Beale
The Lagrange Inversion Theorem provides a formula for the power series of the inverse of an analytic function. We present a straightforward extension to functions with a finite num…
math.NA2025
High order regularization of nearly singular surface integrals
J. Thomas Beale, Svetlana Tlupova
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to eval…
math.NA2024
Extrapolated regularization of nearly singular integrals on surfaces
J. Thomas Beale, Svetlana Tlupova
We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at point…