6 citations · 12 across the 14 of their papers we have counts for
7 papers · 1 filter
On polynomial interpolation in the monomial basis
Zewen Shen, Kirill Serkh
In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde…
Phase function methods for second order inhomogeneous linear ordinary differential equations
Kirill Serkh, James Bremer
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underl…
On the adaptive Levin method
Shukui Chen, Kirill Serkh, James Bremer
The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antider…
Rapid evaluation of Newtonian potentials on planar domains
Zewen Shen, Kirill Serkh
The accurate and efficient evaluation of Newtonian potentials over general 2-D domains is important for the numerical solution of Poisson's equation and volume integral equations.…
Accelerating potential evaluation over unstructured meshes in two dimensions
Zewen Shen, Kirill Serkh
The accurate and efficient evaluation of potentials is of great importance for the numerical solution of partial differential equations. When the integration domain of the potentia…
Fast Computation of Electrostatic Potentials for Piecewise Constant Conductivities
Kyle Bower, Kirill Serkh, Spyros Alexakis +1
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ a…
A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing
Dawei Wang, Kirill Serkh, Christina Christara
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference…