Toby Driscoll: Software

UD links: Software@UD Math; UD Math; MATLAB@UD

Other links: MATLAB Central

The Schwarz-Christoffel Toolbox for MATLAB

The SC Toolbox is a problem-solving environment for computation and interaction with conformal maps to regions bounded by polygons, including unbounded regions, logical quadrilaterals, and channels. It includes a module for the solution of the Laplace equation on such regions with piecewise constant boundary conditions, to ten digits or more in seconds.

Relevant publications:

T. A. Driscoll. A MATLAB Toolbox for Schwarz-Christoffel mapping. ACM Trans. Math. Soft. 22 (1996), pp. 168-186.
T. A. Driscoll. Algorithm 843: Improvements to the Schwarz-Christoffel Toolbox for MATLAB. ACM Trans. Math. Soft. 31 (2005), 239-251.

The chebop system

The chebop toolbox for MATLAB is an extension of the chebfun system for numerical computation with functions. A chebop is an abstraction of a numerically realized differential or integral operator. Using familiar MATLAB syntax such as \ and eigs, solutions to linear differential boundary value or eigenvalue problems can be obtained with ten or more digits of precision automatically.

Relevant publications:

T. A. Driscoll, F. Bornemann and L. N. Trefethen. The chebop system for automatic solution of differential equations, submitted to BIT.

Other MATLAB software

The function coarserefine.m, as support for this paper on adaptive radial basis function methods. You can find a more advanced variation, for Burgers' equation, at this link.
Some random utilities for MATLAB:

latex		Output a matrix in a format that can be pasted into a LaTeX environment.
gslope		Click on two points and get the slope between them computed automatically.
unplot		Remove the most recently drawn graphics object(s).
wysiwyg		Preview a figure window at the size it will be output in hardcopy.

There are a few others listed in my MATLAB Central area.