Special Session 71: Progress in Partial Differential Equations of Mathematical Physics: Theory and Methods

New transform methods for doubly connected planar domains
Jesse Hulse
University of Manitoba
Canada
Co-Author(s):    
Abstract:
A new transform-based technique that generalizes the Unified Transform Method is developed for bounded doubly connected domains as a novel way to numerically solve boundary value problems for holomorphic functions and solutions to the Laplacian. This work utilizes the Szeg\"{o} kernel for the annulus and generalizes methods for circular and simply connected domains developed by Crowdy (2015) and H., Lanzani, Llewellyn Smith, and Luca (2025). Time permitting, an application will be shown.