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 ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

In this Python astrophysics tutorial, I walk you through calculating the gravitational field produced by a ring of mass. Using numerical methods and Python libraries, we explore how to compute ...

We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients.

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 ...

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 ...

Error estimates for fully discretized particle or simulation methods for multidimensional Vlasov-Poisson systems are provided. The treatment requires stability ...