**fem1d_heat_explicit_test**,
a MATLAB code which
calls fem1d_heat_explicit(), which
solves the time-dependent 1D heat equation, using the finite element
method in space, and an explicit version of the method of lines to handle
integration in time.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

fem1d_heat_explicit, a MATLAB code which uses the finite element method (FEM) and explicit time stepping to solve the time dependent heat equation in 1D.

- fem1d_heat_explicit_test.m, calls all the tests.
- fem1d_heat_explicit_test.sh, runs all the tests.
- fem1d_heat_explicit_test.txt, the output file.

- fem1d_heat_explicit_test01.m, runs test 1;
- fem1d_heat_explicit_test02.m, runs test 2;
- fem1d_heat_explicit_test03.m, runs test 3;

**TEST01** runs with initial condition 50 everywhere, boundary conditions
of 90 on the left and 70 on the right, and no right hand side source term.

- bc_test01.m, enforces the boundary conditions.
- h_test01.txt, the computed H data.
- ic_test01.m, enforces the initial condition.
- k_test01.m, sets the conductivity.
- plot_test01.png, a PNG image of the solution.
- rhs_test01.m, supplies the right hand side source term.
- t_test01.txt, the T data.
- x_test01.txt, the X data.

**TEST02** uses an exact solution of g(x,t) = exp ( - t ) .* sin ( sqrt ( k ) * x ).

- bc_test02.m, enforces the boundary conditions.
- exact_test02.m, evaluates the exact solution.
- g_test02.txt, the exact data.
- h_test02.txt, the computed H data.
- ic_test02.m, enforces the initial condition.
- k_test02.m, sets the conductivity.
- plot_test02.png, a PNG image of the solution.
- rhs_test02.m, supplies the right hand side source term.
- t_test02.txt, the T data.
- x_test02.txt, the X data.

**TEST03** runs on the interval -5 <= X <= 5, with initial condition 15 on the
entire left and 25 on the entire right. The solution should settle down to a
straight line from the left boundary to the right.

- bc_test03.m, enforces the boundary conditions.
- h_test03.txt, the computed H data.
- ic_test03.m, enforces the initial condition.
- k_test03.m, sets the conductivity.
- plot_test03.png, a PNG image of the solution.
- rhs_test03.m, supplies the right hand side source term.
- t_test03.txt, the T data.
- x_test03.txt, the X data.