% Sideways Heat Equation Tools.
%
% Matlab V6 (should also work with Matlab V5)
% Last modified: 14/12-2001.
% Fredrik Berntsson, frber@math.liu.se.
%
%
% Demonstration:
%
% shedemo - A simple script which creates a model problem and
% solves it.
% shedemo2 - Same as shedemo.
% shedemo3 - A short demonstration of other methods for solving
% the sideways heat equation. (TSVD and Tikhonov regu.)
% shedemo4 - The tools developed for solving the sideways heat equation
% can be used for continuously monitoring the surface
% temperature. In this demo we demonstrate a very useful
% (and simple) technique.
% shedemo5 - The surface temperature on a particle board is computed
% using interior measurements. This test uses actual measured
% data.
%
% Test functions:
%
% bell0 - A Gaussian bell.
% bou0 - A thin spike.
% bou2 - Similar to bou0 but with two peaks.
% box0 - A function which looks like a square
% box. This leads to a discontinous solution
% of the sideways heat equation..
% box1 - A smoothed box.
% bran0 - A random signal starting and ending with zero.
% bsin0 - A sine shaped wave.
%
%
% Sideways solvers:
%
%* id0rk45 - Computes the solution to the sideways heat
% equation given data at x=1. The data is filtered
% and the time derivative is replaced by a
% central difference approximation. Space integration
% is preformed using an explicit Runge-Kutta method.
% ifftrk45 - Same as id0rk45 except that we calculate the time
% derivative i Fourier space. Regularization is
% accomplished by cutting off high frequency parts.
% imeyrk45 - Same as id0rk45 except that we use a Galerkin
% approximation of the time derivative, based on
% Meyer wavelets.
% iwavrk45 - Same as imeyrk45 except that we use the different
% wavetets available in wavelet toolbox.
%
% fourier_solve - Explicit computation of the symbol of the
% solution operator using the Fourier transform.
%
%
% Direct problem solvers:
%
% explhs - Calculates the solution at x=1 given data at x=0,
% using an explicit method.
% crnhs - Same as above except that we use the Crank-Nicholson
% implicit scheme.
% crnhs2 - Same as crnhs except that the Cauchy data [g,h] are
% computed at a point 0