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# Linear ODE
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linear = (u, p, t) -> (p * u)
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linear_analytic = (u0, p, t) -> u0 * exp (p * t)
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- """
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+ @doc doc """
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Linear ODE
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```math
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- \\ frac{du}{dt} = αu
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+ \f rac{du}{dt} = αu
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```
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- with initial condition ``u_0=\\ frac{1}{2}``, ``α=1.01``, and solution
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+ with initial condition ``u_0=\f rac{1}{2}``, ``α=1.01``, and solution
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```math
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u(t) = u_0 e^{αt}
@@ -19,14 +19,14 @@ with Float64s. The parameter is ``α``
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prob_ode_linear = ODEProblem (ODEFunction (linear, analytic = linear_analytic),
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1 / 2 , (0.0 , 1.0 ), 1.01 )
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- """
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+ @doc doc """
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Linear ODE
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```math
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- \\ frac{du}{dt} = αu
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+ \f rac{du}{dt} = αu
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```
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- with initial condition ``u_0=\\ frac{1}{2}``, ``α=1.01``, and solution
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+ with initial condition ``u_0=\f rac{1}{2}``, ``α=1.01``, and solution
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```math
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u(t) = u_0 e^{αt}
@@ -39,14 +39,14 @@ prob_ode_bigfloatlinear = ODEProblem(ODEFunction(linear, analytic = linear_analy
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f_2dlinear = (du, u, p, t) -> (@. du = p * u)
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f_2dlinear_analytic = (u0, p, t) -> @. u0 * exp (p * t)
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- """
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+ @doc doc """
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4×2 version of the Linear ODE
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```math
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- \\ frac{du}{dt} = αu
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+ \f rac{du}{dt} = αu
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```
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- with initial condition ``u_0`` as all uniformly distributed random numbers,
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+ with initial condition ``u_0`` as all uniformly distributed random numbers,
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``α=1.01``, and solution
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```math
@@ -58,14 +58,14 @@ with Float64s
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prob_ode_2Dlinear = ODEProblem (ODEFunction (f_2dlinear, analytic = f_2dlinear_analytic),
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rand (4 , 2 ), (0.0 , 1.0 ), 1.01 )
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- """
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+ @doc doc """
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100×100 version of the Linear ODE
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```math
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- \\ frac{du}{dt} = αu
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+ \f rac{du}{dt} = αu
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```
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- with initial condition ``u_0`` as all uniformly distributed random numbers,
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+ with initial condition ``u_0`` as all uniformly distributed random numbers,
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``α=1.01``, and solution
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```math
@@ -78,14 +78,14 @@ prob_ode_large2Dlinear = ODEProblem(
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ODEFunction (f_2dlinear, analytic = f_2dlinear_analytic),
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rand (100 , 100 ), (0.0 , 1.0 ), 1.01 )
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- """
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+ @doc doc """
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4×2 version of the Linear ODE
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```math
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- \\ frac{du}{dt} = αu
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+ \f rac{du}{dt} = αu
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```
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- with initial condition ``u_0`` as all uniformly distributed random numbers,
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+ with initial condition ``u_0`` as all uniformly distributed random numbers,
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``α=1.01``, and solution
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```math
@@ -101,14 +101,14 @@ prob_ode_bigfloat2Dlinear = ODEProblem(
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big (1.01 ))
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f_2dlinear_notinplace = (u, p, t) -> p * u
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- """
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+ @doc doc """
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4×2 version of the Linear ODE
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```math
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- \\ frac{du}{dt} = αu
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+ \f rac{du}{dt} = αu
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```
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- with initial condition ``u_0`` as all uniformly distributed random numbers,
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+ with initial condition ``u_0`` as all uniformly distributed random numbers,
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``α=1.01``, and solution
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```math
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