Update Simple_Differential_Equation.ipynb

[jpfairbanks]

Avoid using start as a variable in example

[jpfairbanks]

I went through this example and got this error if we avoid the variable start it shouldn't happen.

julia> ode45(f, start, trange)
ERROR: MethodError: `/` has no method matching /(::Function, ::Float64)
Closest candidates are:
  /(::Float64, ::Float64)
  /(::Complex{T<:Real}, ::Real)
  /(::BigFloat, ::Union{Float16,Float32,Float64})
  ...
 in make_consistent_types at /home/james/.julia/v0.4/ODE/src/ODE.jl:124
 in oderk_fixed at /home/james/.julia/v0.4/ODE/src/runge_kutta.jl:180
 in oderk_fixed at /home/james/.julia/v0.4/ODE/src/runge_kutta.jl:168
 in ode45 at /home/james/.julia/v0.4/ODE/src/runge_kutta.jl:163

[acroy]

Using start as a variable shouldn't cause problems. Did you try to restart julia?

In any case it is good practice to post a complete example (possibly including the versions of Julia and ODE), which shows the error. If I do the following in Julia v0.4 and ODE v0.2.1:

using ODE

function f(t, y)
           # Extract the components of the y vector
           (x, v) = y

           # Our system of differential equations
           x_prime = v
           v_prime = -x

           # Return the derivatives as a vector
           [x_prime; v_prime]
end

const start = [0.0; 0.1]
time = 0:0.1:4*pi

t, y = ode45(f, start, time);

There is no problem:

julia> y[end]
2-element Array{Float64,1}:
 -0.00663187
  0.0997793 
julia> t[end]
12.5

[pjpmarques]

Hi. Any conclusion on this? start shouldn't be the cause of the problem.

[ChrisRackauckas]

start may not be the cause of the problem due to ODE, but having a variable named start can easily cause problems in other cases. @jpfairbanks probably had a problem due to something defining an array interface (which is why the error is due to a function).

Because these are so common, it's a good idea to not have start as a variable in an example since it has a common other use and is thus begging for trouble. Changing the name to starty is harmless but gets rid of any possibility of this overlap. I'll wait for a second opinion but vote to merge.

@pwl @acroy @mauro3 ?

[ChrisRackauckas]

Given the +1's and that it's pretty harmless, I'm merging.