Physics World

Neural networks discover unstable singularities in fluid systems

The Navier–Stokes partial differential equation was developed in the early 19th century by Claude-Louis Navier and George ...
Quanta Magazine

Latest Neural Nets Solve World’s Hardest Equations Faster Than Ever Before

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 ...
JSTOR Daily

Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions

Abstract. We design a numerical scheme for solving the Multi-step Forward Dynamic Programming (MDP) equation arising from the time-discretization of backward stochastic differential equations. The ...
JSTOR Daily

Monotone Iterative Technique via Initial Time Different Coupled Lower and Upper Solutions for Fractional Differential Equations

S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon (1993). A. Yakar, and H. Kutlay, A ...
Quanta Magazine

New Quantum Algorithms Finally Crack Nonlinear Equations

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...
lse

Partial Differential Equations

This course is available on the BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course ...