Minor example doc tweaks

examples/evp_1d_mathieu/mathieu_evp.py

@@ -7,6 +7,9 @@
 We use a Fourier basis to solve the EVP:
     dx(dx(y)) + (a - 2*q*cos(2*x))*y = 0
 where 'a' is the eigenvalue. Periodicity is enforced by using the Fourier basis.
+
+To run and plot:
+    $ python3 mathieu_evp.py
 """
 
 import numpy as np

examples/evp_1d_rayleigh_benard/rayleigh_benard_evp.py

@@ -1,7 +1,7 @@
 """
 Dedalus script for calculating the maximum linear growth rates in no-slip
 Rayleigh-Benard convection over a range of horizontal wavenumbers. This script
-demonstrates solving a 1D eigenvalue problem in a cartesian domain. It can
+demonstrates solving a 1D eigenvalue problem in a Cartesian domain. It can
 be ran serially or in parallel, and produces a plot of the highest growth rate
 found for each horizontal wavenumber. It should take a few seconds to run.
 

examples/evp_1d_waves_on_a_string/waves_on_a_string.py

@@ -1,8 +1,8 @@
 """
 Dedalus script computing the eigenmodes of waves on a clamped string.
 This script demonstrates solving a 1D eigenvalue problem and produces
-a plot of the relative error of the eigenvalues.  It should take just
-a few seconds to run (serial only).
+plots of the first few eigenmodes and the relative error of the eigenvalues.
+It should take just a few seconds to run (serial only).
 
 We use a Legendre basis to solve the EVP:
     s*u + dx(dx(u)) = 0
@@ -14,6 +14,9 @@
 Here we choose to use a first-order formulation, putting one tau term
 on an auxiliary first-order variable and another in the PDE, and lifting
 both to the first derivative basis.
+
+To run and plot:
+    $ python3 waves_on_a_string.py
 """
 
 import numpy as np

examples/evp_shell_rotating_convection/rotating_convection.py

@@ -21,6 +21,9 @@
 if the resolution is increased. For the given resolutions, the eigenvalues agree
 with Table 1 of [1] to several digits of precision.
 
+To run and print the calculated eigenvalues:
+    $ python3 rotating_convection.py
+
 References:
     [1]: P. Marti, M. A. Calkins, K. Julien, "A computationally
          efficient spectral method for modeling coredynamics,"

examples/ivp_1d_kdv_burgers/kdv_burgers.py

@@ -6,6 +6,9 @@
 
 We use a Fourier basis to solve the IVP:
     dt(u) + u*dx(u) = a*dx(dx(u)) + b*dx(dx(dx(u)))
+
+To run and plot:
+    $ python3 kdv_burgers.py
 """
 
 import numpy as np

examples/ivp_2d_rayleigh_benard/rayleigh_benard.py

@@ -1,9 +1,9 @@
 """
 Dedalus script simulating 2D horizontally-periodic Rayleigh-Benard convection.
-This script demonstrates solving a 2D cartesian initial value problem. It can
+This script demonstrates solving a 2D Cartesian initial value problem. It can
 be ran serially or in parallel, and uses the built-in analysis framework to save
 data snapshots to HDF5 files. The `plot_snapshots.py` script can be used to
-produce plots from the saved data. It should take about a cpu-minute to run.
+produce plots from the saved data. It should take a few cpu-minutes to run.
 
 The problem is non-dimensionalized using the box height and freefall time, so
 the resulting thermal diffusivity and viscosity are related to the Prandtl

examples/lbvp_2d_poisson/poisson.py

@@ -10,6 +10,9 @@
 
 For a scalar Laplacian on a finite interval, we need two tau terms. Here we
 choose to lift them to the natural output (second derivative) basis.
+
+To run and plot:
+    $ python3 poisson.py
 """
 
 import numpy as np

examples/nlbvp_ball_lane_emden/lane_emden.py

@@ -1,8 +1,8 @@
 """
 Dedalus script solving the Lane-Emden equation. This script demonstrates
 solving a spherically symmetric nonlinear boundary value problem inside the
-ball. It should be ran serially, should converge within roughly a dozen
-iterations, and should take just a few seconds to run.
+ball. It should converge within roughly a dozen Newton iterations, and produces a
+plot of the solution. I should take just a few seconds to run (serial only).
 
 In astrophysics, the Lane-Emden equation is a dimensionless form of Poisson's
 equation for the gravitational potential of a Newtonian self-gravitating,
@@ -30,6 +30,9 @@
 For a scalar Laplacian in the ball, we need a single tau term. Here we choose
 to lift it to the original (k=0) basis.
 
+To run and plot:
+    $ python3 lane_emden.py
+
 References:
     [1]: http://en.wikipedia.org/wiki/Lane–Emden_equation
     [2]: J. P. Boyd, "Chebyshev spectral methods and the Lane-Emden problem,"