We provide a new analytical approach to operator splitting for equations of the type u t = Au + uu x where A is a linear differential operator such that the equation is well-posed. Particular examples ...

We were always taught that the fundamental passive components were resistors, capacitors, and inductors. But in 1971, [Leon Chua] introduced the idea of a memristor — a sort of resistor with memory.

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

A superexponentially convergent method for solving the Sturm-Liouville problem with Legendre's differential operator is given. The presented method (called the FD-method) is based on the coefficient ...

This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

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 ...

Modeling how cars deform in a crash, how spacecraft responds to extreme environments, or how bridges resist stress could be made thousands of times faster thanks to new artificial intelligence that ...