2025 Colloquium: Numerical Methods for PDEs and Their Applications

Summary

Partial differential equations (PDEs) are central to many approaches to modeling our world. For complex phenomena, partial differential equations can be derived, but analytic solutions are often harder to come by. Numerical methods help bridge the gap between abstract equations and quantitative predictions, allowing PDEs to be used in a wide range of application areas. This colloquium highlights recent work in numerical methods by research experts around the world. As a bonus presentation, you'll get a developer's view on how finite element method (FEM) functionality is approached as a core part of Wolfram Language. The colloquium covers advanced topics, but anyone curious about differential equations can benefit from the presentations.