### matlab *.m files to solve the nonlinear Schroedinger equation.

This solves the Nonlinear Schroedinger equation with explicit
time-stepping, and spectrally-computed space derivatives. explicit_schroedinger.m
** Warning! It's a numerically unstable scheme! **

This solves the Nonlinear Schroedinger equation with implicit
time-stepping, and spectrally-computed space derivatives. implicit_schroedinger.m

This solves the Nonlinear Schroedinger equation using a splitting
method for the
time-stepping, and spectrally-computed space derivatives. split_schroedinger.m

This solves the semilinear heat equation equation with implicit
time-stepping, and spectrally-computed space derivatives. implicit_nonlinear_heat.m

This solves the semilinear heat equation using a splitting
method for the
time-stepping, and spectrally-computed space derivatives. split_nonlinear_heat.m

For more about spectral methods, pseudospectral methods, and computing the nonlinear Schroedinger equation, have
a look at the
lovely notes
of
Rob Almgren.