08-Jan-2022 09:20:50

schroedinger_linear_pde_test
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Solve the linear Schroedinger PDE
  using the method of lines
  and various ODE solvers.

  Parameter values:
    alpha = 0.5
    c1    = 1
    c2    = 0.1
    delta = 25
    gamma = 1
    t0    = 0
    xmin  = -20
    xmax  = 80

schroedinger_linear_ode45
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Solve the linear Schroedinger PDE using ode45()
  Solve the linear Schroedinger equation in 1D,
    du/dt = i uxx + i gamma |u|^2 u
  over the spatial interval:
    -20 <= x <= 80
  and time interval
     0 <= t <= 44.0
  with Neumann boundary conditions:
    u'(-20) = 0.0
    u'(80) = 0.0
  and parameter:
    gamma = 1
  and initial condition
    u(0,x) = sqrt(2 alpha/gamma) * 
    ( exp(0.5 i c1 x       ) sech( sqrt(alpha) x )
    + exp(0.5 i c2 (x-delta) sech( sqrt(alpha)(x-delta) ).
  and NX equally spaced nodes in X,
  using ode45().
  Use 201 nodes, with dx=0.5 in space interval [-20,80]
  Time interval is [0,10]
  Number of (variable size) time steps = 273
  Graphics saved as "schroedinger_linear_ode45_initial.png"
  Graphics saved as "schroedinger_linear_ode45_midway.png"
  Graphics saved as "schroedinger_linear_ode45_final.png"
  Graphics saved as "schroedinger_linear_ode45_conservation.png"

schroedinger_linear_ode45
  Normal end of execution.

schroedinger_linear_midpoint
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Solve the linear Schroedinger PDE using midpoint()
  Solve the linear Schroedinger equation in 1D,
    du/dt = i uxx
  over the spatial interval:
    -20 <= x <= 80
  using 201 equally spaced spatial nodes
  and time interval
     0 <= t <= 44.0
  using 250 equally spaced time steps
  with Neumann boundary conditions:
    u'(-20) = 0.0
    u'(80) = 0.0
  and parameter:
    gamma = 1
  and initial condition
    u(0,x) = sqrt(2 alpha/gamma) * 
    ( exp(0.5 i c1 x       ) sech( sqrt(alpha) x )
    + exp(0.5 i c2 (x-delta) sech( sqrt(alpha)(x-delta) ).
  using midpoint().
  Use 201 nodes, with dx=0.5 in space interval [-20,80]
  Use 250 steps, with dt=0.04 in time interval [0,10]
  Graphics saved as "schroedinger_linear_midpoint_initial.png"
  Graphics saved as "schroedinger_linear_midpoint_midway.png"
  Graphics saved as "schroedinger_linear_midpoint_final.png"
  Graphics saved as "schroedinger_linear_midpoint_conservation.png"

schroedinger_linear_midpoint
  Normal end of execution.

schroedinger_linear_pde_test
  Normal end of execution.
08-Jan-2022 09:22:16