### matlab *.m files to solve PDEs using spectral methods.

If these programs strike you as slightly slow, they are. They would
run more quickly if they were coded up in C or fortran. As matlab
programs, would run more quickly if they were compiled using the
matlab compiler and then run within matlab.

Here's a script from the March 20 class discussing power spectra of
various functions
class_mar20.m It uses the script
find_spec.m .

Here's a script from the March 27 class comparing finite difference
approximations of derivatives to spectral approximations of derivatives.
class_mar27.m It uses the script
d_mid.m,
f.m,
and
fdiff.m and

All of the following codes are on [0,2 pi] and assume periodic boundary
conditions.

Here's a script from the April 1 class comparing different
spectral approaches to solving the heat equation.
class_apr1.m It uses the scripts
heat4.m, heat5.m, heat6.m, and heat7.m below.

This solves the heat equation by treating the linear term explicitly
heat4.m

This solves the heat equation by treating the linear term implicitly
heat5.m

This solves the heat equation by Crank-Nicolson
heat6.m

This solves the heat equation exactly
heat7.m

This solves Burger's equation by treating the nonlinearity explicitly
and evolving the linear term exactly
burgers2.m
It needs subroutine
convolve.m Here's a script testing it out:
test_burgers2.m

This solves Burger's equation by treating both the linear term and
the nonlinear term explicitly
burgers2a.m
It needs subroutine
convolve.m Here's a script testing it out:
test_burgers2a.m

This solves Burger's equation by treating the linear term implicitly
and
the nonlinear term explicitly
burgers2b.m
It needs subroutine
convolve.m Here's a script testing it out:
test_burgers2b.m

This solves Burger's equation via an integrating factor method.
burgers3.m
It needs subroutine
convolve.m Here's a script testing it out:
test_burgers3.m

This solves the cubic Schroedinger equation via a splitting method.
split_schroedinger1.m
Here's a script testing it out:
test_schroedinger1.m

This solves the cubic Schroedinger equation via Strang splitting.
split_schroedinger2.m
Here's a script testing it out:
test_schroedinger2.m

This solves the cubic Schroedinger equation via Richardson extrapolation
on Strang splitting
split_schroedinger1.m
Here's a script testing it out:
test_schroedinger3.m