no user facing unicode and tspans in probs

Author: ChrisRackauckas

src/dae_premade_problems.jl

@@ -6,7 +6,7 @@ f = function (tres, y, yp, r)
     r[1] -=  yp[1]
     r[3]  =  y[1] + y[2] + y[3] - 1.0
 end
-u₀ = [1.0, 0, 0]
-du₀ = [-0.04, 0.04, 0.0]
+u0 = [1.0, 0, 0]
+du0 = [-0.04, 0.04, 0.0]
 "DAE residual form for the Robertson model"
-prob_dae_resrob = DAEProblem(f,u₀,du₀)
+prob_dae_resrob = DAEProblem(f,u0,du0)

src/fem_premade_problems.jl

@@ -34,43 +34,43 @@ prob_femheat_diffuse = HeatProblem(analytic_diffuse,Du,f)
 
 
 f = (t,x)  -> zeros(size(x,1))
-u₀ = (x) -> float((abs.(x[:,1]-.5) .< 1e-6) & (abs.(x[:,2]-.5) .< 1e-6)) #Only mass at middle of (0,1)^2
+u0 = (x) -> float((abs.(x[:,1]-.5) .< 1e-6) & (abs.(x[:,2]-.5) .< 1e-6)) #Only mass at middle of (0,1)^2
 """
 Example problem which starts with a Dirac δ cenetered at (0.5,0.5) and solves with ``f=gD=0``.
 This gives the Green's function solution.
 """
-prob_femheat_pure = HeatProblem(u₀,f)
+prob_femheat_pure = HeatProblem(u0,f)
 
 
 f = (t,x,u) -> ones(size(x,1)) - .5u
-u₀ = (x) -> zeros(size(x,1))
+u0 = (x) -> zeros(size(x,1))
 """
 Homogenous reaction-diffusion problem which starts with 0 and solves with ``f(u)=1-u/2``
 """
-prob_femheat_birthdeath = HeatProblem(u₀,f)
+prob_femheat_birthdeath = HeatProblem(u0,f)
 
 
 f = (t,x,u)  -> [ones(size(x,1))-.5u[:,1]   ones(size(x,1))-u[:,2]]
-u₀ = (x) -> ones(size(x,1),2).*[.5 .5] # size (x,2), 2 meaning 2 variables
+u0 = (x) -> ones(size(x,1),2).*[.5 .5] # size (x,2), 2 meaning 2 variables
 """
 Homogenous reaction-diffusion which starts at 1/2 and solves the system ``f(u)=1-u/2`` and ``f(v)=1-v``
 """
-prob_femheat_birthdeathsystem = HeatProblem(u₀,f)
+prob_femheat_birthdeathsystem = HeatProblem(u0,f)
 
 f = (t,x,u)  -> [zeros(size(x,1))    zeros(size(x,1))]
-u₀ = (x) -> [float((abs.(x[:,1]-.5) .< 1e-6) & (abs.(x[:,2]-.5) .< 1e-6)) float((abs.(x[:,1]-.5) .< 1e-6) & (abs.(x[:,2]-.5) .< 1e-6))]  # size (x,2), 2 meaning 2 variables
+u0 = (x) -> [float((abs.(x[:,1]-.5) .< 1e-6) & (abs.(x[:,2]-.5) .< 1e-6)) float((abs.(x[:,1]-.5) .< 1e-6) & (abs.(x[:,2]-.5) .< 1e-6))]  # size (x,2), 2 meaning 2 variables
 """
 Example problem which solves the homogeneous Heat equation with all mass starting at (1/2,1/2) with two different diffusion constants,
 ``D₁=0.01`` and ``D₂=0.001``. Good animation test.
 """
-prob_femheat_diffusionconstants = HeatProblem(u₀,f,D=[.01 .001])
+prob_femheat_diffusionconstants = HeatProblem(u0,f,D=[.01 .001])
 
 f  = (t,x,u)  -> [ones(size(x,1))-.5u[:,1]     .5u[:,1]-u[:,2]]
-u₀ = (x) -> ones(size(x,1),2).*[.5 .5] # size (x,2), 2 meaning 2 variables
+u0 = (x) -> ones(size(x,1),2).*[.5 .5] # size (x,2), 2 meaning 2 variables
 """
 Homogenous reaction-diffusion which starts with 1/2 and solves the system ``f(u)=1-u/2`` and ``f(v)=.5u-v``
 """
-prob_femheat_birthdeathinteractingsystem = HeatProblem(u₀,f)
+prob_femheat_birthdeathinteractingsystem = HeatProblem(u0,f)
 
 """
 `heatProblemExample_grayscott(;ρ=.03,k=.062,D=[1e-3 .5e-3])`
@@ -89,9 +89,9 @@ function heatProblemExample_grayscott(;ρ=.03,k=.062,D=[1e-3 .5e-3])
   f₁(t,x,u)  = u[:,1].*u[:,2].*u[:,2] + ρ*(1-u[:,2])
   f₂(t,x,u)  = u[:,1].*u[:,2].*u[:,2] -(ρ+k).*u[:,2]
   f(t,x,u) = [f₁(t,x,u) f₂(t,x,u)]
-  u₀(x) = [ones(size(x,1))+rand(size(x,1)) .25.*float(((.2.<x[:,1].<.6) &
+  u0(x) = [ones(size(x,1))+rand(size(x,1)) .25.*float(((.2.<x[:,1].<.6) &
           (.2.<x[:,2].<.6)) | ((.85.<x[:,1]) & (.85.<x[:,2])))] # size (x,2), 2 meaning 2 variables
-  return(HeatProblem(u₀,f,D=D))
+  return(HeatProblem(u0,f,D=D))
 end
 
 """
@@ -124,18 +124,18 @@ function heatProblemExample_gierermeinhardt(;a=1,α=1,D=[0.01 1.0],ubar=1,vbar=0
   f(t,x,u) = [f₁(t,x,u) f₂(t,x,u)]
   uss = (ubar +β)/α
   vss = (α/β)*uss.^2
-  u₀(x) = [uss*ones(size(x,1))+startNoise*rand(size(x,1)) vss*ones(size(x,1))] # size (x,2), 2 meaning 2 variables
-  return(HeatProblem(u₀,f,D=D))
+  u0(x) = [uss*ones(size(x,1))+startNoise*rand(size(x,1)) vss*ones(size(x,1))] # size (x,2), 2 meaning 2 variables
+  return(HeatProblem(u0,f,D=D))
 end
 
 f = (t,x,u)  -> ones(size(x,1)) - .5u
-u₀ = (x) -> zeros(size(x,1))
+u0 = (x) -> zeros(size(x,1))
 σ = (t,x,u) -> 1u.^2
 """
 Homogenous stochastic reaction-diffusion problem which starts with 0
 and solves with ``f(u)=1-u/2`` with noise ``σ(u)=10u^2``
 """
-prob_femheat_stochasticbirthdeath = HeatProblem(u₀,f,σ=σ)
+prob_femheat_stochasticbirthdeath = HeatProblem(u0,f,σ=σ)
 
 ## Poisson
 
@@ -163,21 +163,21 @@ with the same ``f``.
 prob_poisson_birthdeath = PoissonProblem(f,numvars=1)
 
 f  = (x,u) -> [ones(size(x,1))-.5u[:,1]     ones(size(x,1))-u[:,2]]
-u₀ = (x) -> .5*ones(size(x,1),2) # size (x,2), 2 meaning 2 variables
+u0 = (x) -> .5*ones(size(x,1),2) # size (x,2), 2 meaning 2 variables
 
 """
 Nonlinear Poisson equation with ``f(u)=1-u/2`` and ``f(v)=1-v`` and initial
 condition homogenous 1/2. Corresponds to the steady state of a humogenous
 reaction-diffusion equation with the same ``f``.
 """
-prob_poisson_birthdeathsystem = PoissonProblem(f,u₀=u₀)
+prob_poisson_birthdeathsystem = PoissonProblem(f,u0=u0)
 
 f  = (x,u) -> [ones(size(x,1))-.5u[:,1]     .5u[:,1]-u[:,2]]
-u₀ = (x) -> ones(size(x,1),2).*[.5 .5] # size (x,2), 2 meaning 2 variables
+u0 = (x) -> ones(size(x,1),2).*[.5 .5] # size (x,2), 2 meaning 2 variables
 
 """
 Nonlinear Poisson equation with ``f(u)=1-u/2`` and ``f(v)=.5u-v`` and initial
 condition homogenous 1/2. Corresponds to the steady state of a humogenous
 reaction-diffusion equation with the same ``f``.
 """
-prob_poisson_birthdeathinteractingsystem = PoissonProblem(f,u₀=u₀)
+prob_poisson_birthdeathinteractingsystem = PoissonProblem(f,u0=u0)

src/ode_premade_problems.jl

@@ -4,18 +4,18 @@ srand(100)
 
 # Linear ODE
 linear = (t,u) -> (1.01*u)
-analytic_linear = (t,u₀) -> u₀*exp(1.01*t)
+analytic_linear = (t,u0) -> u0*exp(1.01*t)
 """
 Linear ODE
 
 ```math
 \\frac{du}{dt} = αu
 ```
 
-with initial condition ``u₀=1/2``, ``α=1.01``, and solution
+with initial condition ``u0=1/2``, ``α=1.01``, and solution
 
 ```math
-u(t) = u₀e^{αt}
+u(t) = u0e^{αt}
 ```
 
 with Float64s
@@ -24,18 +24,18 @@ prob_ode_linear = ODEProblem(linear,1/2,analytic=analytic_linear)
 
 const linear_bigα = parse(BigFloat,"1.01")
 f_linearbig = (t,u) -> (linear_bigα*u)
-analytic_linearbig = (t,u₀) -> u₀*exp(linear_bigα*t)
+analytic_linearbig = (t,u0) -> u0*exp(linear_bigα*t)
 """
 Linear ODE
 
 ```math
 \\frac{du}{dt} = αu
 ```
 
-with initial condition ``u₀=1/2``, ``α=1.01``, and solution
+with initial condition ``u0=1/2``, ``α=1.01``, and solution
 
 ```math
-u(t) = u₀e^{αt}
+u(t) = u0e^{αt}
 ```
 
 with BigFloats
@@ -47,18 +47,18 @@ f_2dlinear = (t,u,du) -> begin
     du[i] = 1.01*u[i]
   end
 end
-analytic_2dlinear = (t,u₀) -> u₀*exp.(1.01*t)
+analytic_2dlinear = (t,u0) -> u0*exp.(1.01*t)
 """
 4x2 version of the Linear ODE
 
 ```math
 \\frac{du}{dt} = αu
 ```
 
-with initial condition ``u₀=1/2``, ``α=1.01``, and solution
+with initial condition ``u0=1/2``, ``α=1.01``, and solution
 
 ```math
-u(t) = u₀e^{αt}
+u(t) = u0e^{αt}
 ```
 
 with Float64s
@@ -72,10 +72,10 @@ prob_ode_2Dlinear = ODEProblem(f_2dlinear,rand(4,2),analytic=analytic_2dlinear)
 \\frac{du}{dt} = αu
 ```
 
-with initial condition ``u₀=1/2``, ``α=1.01``, and solution
+with initial condition ``u0=1/2``, ``α=1.01``, and solution
 
 ```math
-u(t) = u₀e^{αt}
+u(t) = u0e^{αt}
 ```
 
 with Float64s
@@ -94,10 +94,10 @@ end
 \\frac{du}{dt} = αu
 ```
 
-with initial condition ``u₀=1/2``, ``α=1.01``, and solution
+with initial condition ``u0=1/2``, ``α=1.01``, and solution
 
 ```math
-u(t) = u₀e^{αt}
+u(t) = u0e^{αt}
 ```
 
 with BigFloats
@@ -111,10 +111,10 @@ f_2dlinear_notinplace = (t,u) -> 1.01*u
 \\frac{du}{dt} = αu
 ```
 
-with initial condition ``u₀=1/2``, ``α=1.01``, and solution
+with initial condition ``u0=1/2``, ``α=1.01``, and solution
 
 ```math
-u(t) = u₀e^{αt}
+u(t) = u0e^{αt}
 ```
 
 on Float64. Purposefully not in-place as a test.
@@ -175,7 +175,7 @@ Van der Pol Equations
 \\end{align}
 ```
 
-with ``μ=1.0`` and ``u₀=[0,\\sqrt{3}]``
+with ``μ=1.0`` and ``u0=[0,\\sqrt{3}]``
 
 Non-stiff parameters.
 """
@@ -191,7 +191,7 @@ van_stiff = VanDerPol(μ=1e6)
 \\end{align}
 ```
 
-with ``μ=10^6`` and ``u₀=[0,\\sqrt{3}]``
+with ``μ=10^6`` and ``u0=[0,\\sqrt{3}]``
 
 Stiff parameters.
 """
@@ -222,7 +222,7 @@ Hairer Norsett Wanner Solving Ordinary Differential Euations I - Nonstiff Proble
 
 Usually solved on `[0,1e11]`
 """
-prob_ode_rober = ODEProblem(rober,[1.0;0.0;0.0])
+prob_ode_rober = ODEProblem(rober,[1.0;0.0;0.0],[0,1e11])
 
 # Three Body
 const threebody_μ = parse(BigFloat,"0.012277471"); const threebody_μ′ = 1 - threebody_μ
@@ -258,7 +258,7 @@ From Hairer Norsett Wanner Solving Ordinary Differential Euations I - Nonstiff P
 Usually solved on `t₀ = 0.0`; `T = parse(BigFloat,"17.0652165601579625588917206249")`
 Periodic with that setup.
 """
-prob_ode_threebody = ODEProblem(threebody,[0.994, 0.0, 0.0, parse(BigFloat,"-2.00158510637908252240537862224")])
+prob_ode_threebody = ODEProblem(threebody,[0.994, 0.0, 0.0, parse(BigFloat,"-2.00158510637908252240537862224")],[0.0;parse(BigFloat,"17.0652165601579625588917206249")])
 
 # Rigid Body Equations
 
@@ -289,7 +289,7 @@ or Hairer Norsett Wanner Solving Ordinary Differential Euations I - Nonstiff Pro
 
 Usually solved from 0 to 20.
 """
-prob_ode_rigidbody = ODEProblem(rigid,[1.0,0.0,0.9])
+prob_ode_rigidbody = ODEProblem(rigid,[1.0,0.0,0.9],[0;20])
 
 # Pleiades Problem
 
@@ -363,4 +363,4 @@ From Hairer Norsett Wanner Solving Ordinary Differential Euations I - Nonstiff P
 
 Usually solved from 0 to 3.
 """
-prob_ode_pleides = ODEProblem(pleides,[3.0,3.0,-1.0,-3.0,2.0,-2.0,2.0,3.0,-3.0,2.0,0,0,-4.0,4.0,0,0,0,0,0,1.75,-1.5,0,0,0,-1.25,1,0,0])
+prob_ode_pleides = ODEProblem(pleides,[3.0,3.0,-1.0,-3.0,2.0,-2.0,2.0,3.0,-3.0,2.0,0,0,-4.0,4.0,0,0,0,0,0,1.75,-1.5,0,0,0,-1.25,1,0,0],[0;3])