11# Linear ODE
22linear = (u, p, t) -> (p * u)
33linear_analytic = (u0, p, t) -> u0 * exp (p * t)
4- """
4+ @doc doc """
55Linear ODE
66
77```math
8- \\ frac{du}{dt} = αu
8+ \f rac{du}{dt} = αu
99```
1010
11- with initial condition ``u_0=\\ frac{1}{2}``, ``α=1.01``, and solution
11+ with initial condition ``u_0=\f rac{1}{2}``, ``α=1.01``, and solution
1212
1313```math
1414u(t) = u_0 e^{αt}
@@ -19,14 +19,14 @@ with Float64s. The parameter is ``α``
1919prob_ode_linear = ODEProblem (ODEFunction (linear, analytic = linear_analytic),
2020 1 / 2 , (0.0 , 1.0 ), 1.01 )
2121
22- """
22+ @doc doc """
2323Linear ODE
2424
2525```math
26- \\ frac{du}{dt} = αu
26+ \f rac{du}{dt} = αu
2727```
2828
29- with initial condition ``u_0=\\ frac{1}{2}``, ``α=1.01``, and solution
29+ with initial condition ``u_0=\f rac{1}{2}``, ``α=1.01``, and solution
3030
3131```math
3232u(t) = u_0 e^{αt}
@@ -39,14 +39,14 @@ prob_ode_bigfloatlinear = ODEProblem(ODEFunction(linear, analytic = linear_analy
3939
4040f_2dlinear = (du, u, p, t) -> (@. du = p * u)
4141f_2dlinear_analytic = (u0, p, t) -> @. u0 * exp (p * t)
42- """
42+ @doc doc """
43434×2 version of the Linear ODE
4444
4545```math
46- \\ frac{du}{dt} = αu
46+ \f rac{du}{dt} = αu
4747```
4848
49- with initial condition ``u_0`` as all uniformly distributed random numbers,
49+ with initial condition ``u_0`` as all uniformly distributed random numbers,
5050``α=1.01``, and solution
5151
5252```math
@@ -58,14 +58,14 @@ with Float64s
5858prob_ode_2Dlinear = ODEProblem (ODEFunction (f_2dlinear, analytic = f_2dlinear_analytic),
5959 rand (4 , 2 ), (0.0 , 1.0 ), 1.01 )
6060
61- """
61+ @doc doc """
6262100×100 version of the Linear ODE
6363
6464```math
65- \\ frac{du}{dt} = αu
65+ \f rac{du}{dt} = αu
6666```
6767
68- with initial condition ``u_0`` as all uniformly distributed random numbers,
68+ with initial condition ``u_0`` as all uniformly distributed random numbers,
6969``α=1.01``, and solution
7070
7171```math
@@ -78,14 +78,14 @@ prob_ode_large2Dlinear = ODEProblem(
7878 ODEFunction (f_2dlinear, analytic = f_2dlinear_analytic),
7979 rand (100 , 100 ), (0.0 , 1.0 ), 1.01 )
8080
81- """
81+ @doc doc """
82824×2 version of the Linear ODE
8383
8484```math
85- \\ frac{du}{dt} = αu
85+ \f rac{du}{dt} = αu
8686```
8787
88- with initial condition ``u_0`` as all uniformly distributed random numbers,
88+ with initial condition ``u_0`` as all uniformly distributed random numbers,
8989``α=1.01``, and solution
9090
9191```math
@@ -101,14 +101,14 @@ prob_ode_bigfloat2Dlinear = ODEProblem(
101101 big (1.01 ))
102102
103103f_2dlinear_notinplace = (u, p, t) -> p * u
104- """
104+ @doc doc """
1051054×2 version of the Linear ODE
106106
107107```math
108- \\ frac{du}{dt} = αu
108+ \f rac{du}{dt} = αu
109109```
110110
111- with initial condition ``u_0`` as all uniformly distributed random numbers,
111+ with initial condition ``u_0`` as all uniformly distributed random numbers,
112112``α=1.01``, and solution
113113
114114```math
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