Werner M. Seiler (Kassel University, Germany)
Talk: Theoretical and Numerical Analysis of Singular Initial and Boundary Value Problems
Abstract
We consider quasilinear ordinary differential equations both theoretically and numerically. We call an initial or boundary value problem singular, if at the corresponding point the coefficient of a derivative of highest order vanishes. In such a situation, the well-known existence and uniqueness theorems cannot be applied and also classical numerical integrators typically break down in the vicinity of such a singularity. Using a geometric view of a differential equation as a submanifold in a suitable jet bundle, we define an explicit dynamical system on this submanifold and relate questions of existence, (non)uniqueness and regularity of solutions to standard problems in dynamical systems theory. Furthermore, this point of view leads in a straightforward manner to a simple and robust numerical approach to singular initial and boundary value problems. As examples, we will consider classical equations like Lane-Emden or Thomas-Fermi and show how the for applications relevant initial and boundary value problems can be solved in a few lines of Maple code.
Adam Strzebonski (Wolfram Research, USA)
Talk: Recent Symbolic Computation Developments in Mathematica
Abstract
In this talk a general overview of recent improvements in Mathematica symbolic computation capabilities will be presented and some of the improvements will be discussed in more detail. We will focus on new methods for finding exact solutions of systems of equations and inequalities and for solving exact optimization problems, performance improvements in
polynomial algebra functions, and on new functionality for computation over finite fields.
Jon McLoone (Wolfram Research Europe)
Talk: Wolfram’s Vision for Unified Computation
Abstract
The presentation will delve into the philosophy that has been the driving force behind the development of Wolfram Language over the past 35 years, while also shedding light on its current priorities. Additionally, the talk will explore how this philosophy has been applied to the integration of significant advancements in generative AI. To illustrate this alignment, examples from the latest Mathematica 13.3 will be shown.