Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

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 ...

We deal with real preconditioned interval linear systems of equations. We present a new operator, which generalizes the interval Gauss–Seidel operator. Also, based on the new operator and properties ...

We show that a strongly continuous operator semigroup can be associated with the functional differential delay equation \begin{equation*}\tag{(FDE)}\begin{cases}x'(t ...

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...

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 ...