Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

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. A new ...

A partial differential equation (PDE) is a mathematical equation that involves ... unknown function with respect to the independent variables. Some PDEs have exact solutions, but many aren’t easy to ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Differential equations have a long history of analog solutions. We’ve written about memristors and their uses in neural networks.

AMTH 200. Advanced Engineering Mathematics I Method of solution of the first, second, and higher order differential equations (ODEs). Integral transforms including Laplace transforms, Fourier series ...

First, their algorithm advances a solution forward in time by solving ... A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains, ACM Transactions on Graphics ...

Masaki Kashiwara has won the 2025 Abel prize, seen by some as the Nobel of mathematics, for his contributions to algebraic analysis and representation theory ...

The members of the group Geometric Analysis and Partial Differential Equations have broad interests in analysis and geometry. Active research topics include quasiconformal analysis and partial ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...