Domain decomposition methods constitute a fundamental strategy in numerical analysis, enabling the partitioning of large and complex computational problems into smaller, more manageable sub-problems.

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 ...

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

In the collocating volatility (CLV) model, the stochastic collocation technique is used as a convenient representation of the terminal distribution of the market option prices. A specific dynamic is ...

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 ...

In this paper, an efficient approach for the computation of the fair value of a basket option as well as its Greeks is presented. Both European and American options are considered; the determination ...

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 ...