Toda and Liouville systems are central themes in mathematical physics, providing powerful frameworks for understanding integrable structures, nonlinear dynamics and geometric phenomena. Rooted in the ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

Researchers from the Institute of Cosmos Sciences of the University of Barcelona (ICCUB) have developed a new framework based on machine learning ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...