This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

Mean field-type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞ were recently introduced by Lasry and Lions. Under suitable assumptions, ...

An error analysis of approximation of deltas (derivatives of the solution to the Cauchy problem for parabolic equations) by finite differences is given, taking into ...

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 ...

Course Description: This course provides a practical introduction to the Finite Element Method (FEM), with an emphasis on hands-on implementation using Python. It covers the basic theoretical concepts ...