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 ...

Explore numerical methods for solving constant velocity kinematics problems! In this video, we cover how to apply numerical ...

Adaptive finite element methods (AFEM) represent a pivotal advancement in numerical analysis by dynamically refining computational meshes to achieve greater solution accuracy. These methods are ...

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 ...

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem y' = Ay are inside this region, the numerical ...

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

As the name of the "Virtual Engine and Numerical Methods" department suggests, this department combines research activities on the "virtual engine" and on cross-scale numerical methods as virtual test ...

Researchers have developed a numerical model that can re-create the state of Switzerland's Rhône Glacier as it was in 1874 and predict its evolution until the year 2100. This is the longest period of ...

Studying the equations of General Relativity and beyond, both analytically and with state-of-the-art simulations. Novel numerical and mathematical approaches can shed light on the structure and ...