Jesse Hulse
University of Manitoba
Title
Transform Methods for the Laplacian and Complex Helmholtz Equation
Abstract
A new transform-based technique that generalizes the Unified Transform Method is developed for simply connected and doubly connected domains as a novel way to numerically solve boundary value problems for holomorphic functions and harmonic functions. A transform quasi-pair for the complex Helmholtz equation on convex domains will also be discussed. This work utilizes the Szegő kernel for the annulus and generalizes methods for circular domains developed by Crowdy (2015). Applications will be shown. This is joint work with L. Lanzani, S. Llewellyn Smith, and E. Luca.
