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 ...

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 ...

This is a preview. Log in through your library . Abstract A high-resolution numerical scheme for the computation of viscous shock layers is introduced. The novel feature consists in the use of ...

Optimal control problems, which form a central pillar in applied mathematics and engineering, involve determining control strategies that steer physical, economic or biological systems to achieve a ...

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 ...

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.

This course provides a more advanced mathematical treatment of the topics covered in 98.481, with extensive application of computer techniques to numerical problem solving that is applicable to ...