Various Consequences

Background and Motivation The problem I am interested in: leverage high-level symbol manipulation capabilities in a computer algebra sys...

I posted a while back on solving Burgers' equation on a moving grid . The same coordinate transformation techniques applied there can be...

Solving Burgers' equation on a moving grid is a way to handle moving fronts or shocks by adapting the grid to the solution at each ti...

I've written a couple posts demonstrating the use of Maxima to calculate finite difference expressions of various varieties ( complex s...

I wrote a while back about using Maxima to derive asymmetric complex step finite difference expressions for derivatives. The basic approac...

Gilbert Strang discusses the use of a neat built-in function in Octave, kron() , that's pretty useful for doing multidimensional finite ...

Boole, George. "A Treatise on the Calculus of Finite Differences", Macmillan and Co., 1872. The public domain and Google books i...

In image processing the discrete difference operators to calculate gradients and second derivatives are called "masks". They are o...

I can't really decide on the best way to treat the different channels (red, green, blue) in a color image when doing edge detection. I...

To solve Laplace's equation with a complex step finite difference we needed to develop asymmetric difference relations to solve on the ...

We showed in an earlier post that approximating first derivatives with complex steps leads to a second order accurate formula that avoids t...

A magnetron is a device useful for generating lots of microwave radiation, most homes have magnetron's which use roughly 1kW of microwa...