**schroedinger_linear_pde_test**,
a MATLAB code which
calls schroedinger_linear_pde(), which
solves the complex partial differential equation (PDE)
known as Schroedinger's linear equation:
dudt = i uxx, in one spatial dimension,
with Neumann boundary conditions.

schroedinger_linear_pde, a MATLAB code which solves the complex partial differential equation (PDE) known as Schroedinger's linear equation: dudt = i uxx, in one spatial dimension, with Neumann boundary conditions.

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

- schroedinger_linear_midpoint.m, solves the linear Schroedinger equation using midpoint.
- schroedinger_linear_ode45.m, solves the linear Schroedinger equation using ode45().

- midpoint.m, an implicit midpoint ODE solver.

- schroedinger_linear_midpoint_initial.png, the solution at the initial time.
- schroedinger_linear_midpoint_midway.png, the solution at the midway time.
- schroedinger_linear_midpoint_final.png, the solution at the final time.

- schroedinger_linear_ode45_initial.png, the solution at the initial time.
- schroedinger_linear_ode45_midway.png, the solution at the midway time.
- schroedinger_linear_ode45_final.png, the solution at the final time.