3 papers
math.NA2026
The lightning method for the heat equation
Hunter La Croix, Alan E. Lindsay
This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of lin…
math.NA2025
High-order integral methods for the Neumann Green's function: applications to capture and signaling problems in two dimensions
Sanchita Chakraborty, Jeremy Hoskins, Alan E. Lindsay
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves bo…
math.AP2025
The effect of target orientation on the mean first passage time of a Brownian particle to a small elliptical absorber
Sanchita Chakraborty, Theodore Kolokolnikov, Alan E. Lindsay
We develop a high order asymptotic expansion for the mean first passage time (MFPT) of the capture of Brownian particles by a small elliptical trap in a bounded two dimensional reg…