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

This paper is concerned with numerical methods for a class of two-dimensional quasilinear elliptic boundary value problems. A compact finite difference method with a nonisotropic mesh is proposed for ...

Finite-difference approximations for the first derivative, valid halfway between equidistant gridpoints, are in general much more accurate than the corresponding approximations, which are valid at ...

Finite-Difference Time-Domain (FDTD) methods have become a cornerstone in the numerical solution of Maxwell’s equations, enabling detailed electromagnetic analysis across a wide range of applications.

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 ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...