Revising Chris Rackauckas's "exp_euler_test.jl" from Julia 0.6 so it works in Julia 1.1

_ex_Eulers_WORKS.jl

########################################################
# Revising Chris Rackauckas's "exp_euler_test.jl" from
# Julia 0.6 so it works in Julia 1.1
########################################################
# 
# Original 0.6 code from:
# 
# ChrisRackauckas/exp_euler_test.jl
# https://gist.github.com/ChrisRackauckas/cf91f4575b0587a45c72620384612b82
# This works in Julia 0.6
# But DOESN'T WORK IN JULIA 1.1
########################################################

# Pkg.add("SpecialMatrices") # Only need to run the first time
using SpecialMatrices, DiffEqBase
A = Strang(11)
function g(t,u)
  for i in eachindex(u)
    2 - u[i]
  end
  u
end
u0 = zeros(11); u0[6] = 10
tspan = (0.0,10.0)
SplitODEProblem((A,g),u0,tspan)

########
# This represents the diffusion of some chemical which has a source
# A lot starts that the middle (u0[6])
# What you should see is it should diffuse to the other places
# And slowly evenly rise
# If it's run for long enough, it should become flat at u=2 across the domain

########################################################
# End of Chris's stuff
########################################################



#######################################################
# This version WORKS in Julia 1.1,
# as of 2019-04-18
#######################################################

#######################################################
# Mac Terminal command line:
# > julia --version
# julia version 1.1.0
#
# > which julia
# /usr/local/bin/julia
#
# # Show the symbolic link to make Julia 1.1 run from
# # Mac Terminal Command line
# > ls -l /usr/local/bin/julia
# lrwxr-xr-x  1 root  wheel  63  1 Apr 09:52 
# /usr/local/bin/julia -> 
# /Applications/Julia-1.1a.app/Contents/Resources/julia/bin/julia
#
# # To run, type:
# > julia 
#######################################################

# Install the libraries
using Pkg
# Only need to run the first time
Pkg.add("DifferentialEquations")
Pkg.add("DiffEqOperators")
Pkg.add(Pkg.PackageSpec(url = "https://github.com/ChrisRackauckas/EllipsisNotation.jl")) # seems to be dependency for SpecialMatrices?
Pkg.add(Pkg.PackageSpec(url = "https://github.com/JuliaMatrices/SpecialMatrices.jl"))    # for Strang()

# Use the libraries
#using DiffEqBase            # solve() crashes with just this
using DifferentialEquations  # for solve() to not crash (?)
using DiffEqOperators				 # for DiffEqArrayOperator
using SpecialMatrices        # for Strang()
using Plots                  # for plot()


# Define the linear and nonlinear part of the ODE as functions

# Explanation of "!" in function names:
# http://julia.cookbook.tips/doku.php?id=baffling
# Julia recommends a “collaborative” model, where functions that modify their arguments
# should be named with a trailing '!'. Functions without it may or may not modify their
# passed arguments -- well, unless the passed arguments are native primitives and not 
# objects.

# Define the linear part of the problem
# A = Strang(11)
A = Matrix(Strang(11))
f1!(du,u,p,t) = DiffEqArrayOperator(A)

# Define the nonlinear part of the problem
function g1!(du,u,p,t)
  for i in eachindex(u)
    du[i] = 2 - u[i]
  end
end	

# Initial conditions of the changing vector "u"
u0 = zeros(11); u0[6] = 10

# Start and end of timespan over which to integrate
tspan = (0.0,10.0)

# This works in Julia 1.1
prob2 = SplitODEProblem(f1!,g1!,u0,tspan)
sol2 = solve(prob2)
plot(sol2)

# Print value of u[6] through timeseries
for i in eachindex(sol2.u)
	print(sol2.u[i][6])
	print("\n")
end

This code modifies the original gist from Chris Rackauckas, originally posted at: https://gist.github.com/ChrisRackauckas/cf91f4575b0587a45c72620384612b82