The aim of this course is to provide an introduction to modern methods for studying nonlinear partial differential equations. The content of the course, which can change from time to time, is built ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

The study of wave phenomena by means of mathematical models often leads to a certain class of nonlinear partial differential equations referred to as integrable systems. My main area of research deals ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

Abstract: Problems involving the classical linear partial differential equations of mathematical physics can be reduced to algebraic ones of a very much simpler structure by replacing the ...

Backward Stochastic Differential Equations (BSDEs ... of G-BSDEs but also contributes to the broader field of nonlinear stochastic analysis[3]. Additionally, the application of BSDEs in financial ...

Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, NY 10012, USA ...

Abstract: The main purpose of this paper is to present a reasonably complete picture of the results of the first phase of some recent research on the properties of solutions of nonlinear functional ...

They work through the list to rule in and rule out which diagnosis is the best fit. This process is called "differential diagnosis." They may order additional tests or imaging to pinpoint the best ...

In a mesmerising blend of art and mathematics, a research student from University College London (UCL) has recently gained widespread attention for creating intricate images solely through ...