In this tutorial, I demonstrate how to solve boundary value differential equations using the Finite Difference Method in Python. Learn step-by-step how to implement this numerical technique, ...

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 ...

Since its first introduction in 1966, the Finite Difference Time Domain (FDTD) method has been widely used as a tool for solving complex electromagnetic problems. For FDTD, Maxwell’s equations are ...

A new finite difference scheme is presented for solving two-dimensional, transient, incompressible Navier-Stokes problems on a bounded simply-connected region for which there exists a C 2 invertible ...

My main research interests are in developing, analyzing, and implementing numerical methods, in particular for solving PDEs to high orders of accuracy. Such methods include pseudospectral and high ...

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 ...