Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error ...

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...

Analysis and implementation of numerical methods for random processes: random number generators, Monte Carlo methods, Markov chains, stochastic differential equations, and applications. Recommended ...

This paper is devoted to the numerical solution of the axially symmetric linear sloshing problem. A mathematical model of linear sloshing in a tank filled by an inviscid incompressible liquid is ...

Methods for simulating sharp interfaces. Marker particle, level set, fast marching, volume of fluid, and phase field methods. Recommended text: Level Set Methods and Fast Marching Methods: Evolving ...

What Are FEM, FDM and FVM? FEM, FDM and FVM differ from one another in important ways. Understanding these distinctions is key to selecting the method most appropriate for your purposes. The ...