### matlab *.m files to solve the heat equation.

If these programs strike you as slightly slow, they are. They would
run more quickly if they were coded up in C or fortran and then
compiled on hans. As matlab programs, would run more quickly if they
were compiled using the matlab compiler and then run within matlab.
As it is, they're faster than anything maple could do.

This solves the heat equation with explicit time-stepping, and finite-differences
in space.
heat1.m

A diary where heat1.m is used.

This solves the heat equation with implicit time-stepping, and finite-differences
in space.
heat2.m
At each time step, the linear problem Ax=b is solved with an LU decomposition.
This needs subroutines
my_LU.m ,
down_solve.m, and
up_solve.m.
Compare this routine to heat3.m and verify that it's too slow to bother with.

This solves the heat equation with implicit time-stepping, and finite-differences
in space.
heat3.m
At each time step, the linear problem Ax=b is solved with a periodic
tridiagonal routine.
This needs subroutines
periodic_tridiag.m and
tri_diag.m.

A diary where heat3.m is used.

This solves the periodic heat equation with Crank Nicolson time-stepping, and finite-differences
in space.
heat_cn.m
At each time step, the linear problem Ax=b is solved with a periodic
tridiagonal routine.
This needs subroutines
periodic_tridiag.m and
tri_diag.m.

This solves the heat equation with Neumann boundary conditions with
Crank Nicolson time-stepping, and finite-differences
in space.
neumann_heat_cn.m
At each time step, the linear problem Ax=b is solved with a
tridiagonal routine.
This needs subroutine
tri_diag.m.

This solves the heat equation with explicit time-stepping, and spectrally-computed
space derivatives.
heat4.m

A diary where heat4.m is used.

This solves the heat equation with implicit time-stepping, and spectrally-computed
space derivatives.
heat5.m