@@ -49,12 +49,12 @@ prob_ode_fitzhughnagumo = ODEProblem(fitz, [1.0; 1.0], (0.0, 1.0),
4949 (0.7 , 0.8 , 1 / 12.5 , 0.5 ))
5050
5151# Van der Pol Equations
52- @parameters t μ
52+ @parameters μ
5353@variables x (t) y (t)
54- D = Differential (t)
54+
5555eqs = [D (y) ~ μ * ((1 - x^ 2 ) * y - x),
5656 D (x) ~ y]
57- de = ODESystem (eqs; name = :van_der_pol )
57+ de = ODESystem (eqs,t ; name = :van_der_pol ) |> structural_simplify |> complete
5858van = ODEFunction (de, [y, x], [μ], jac = true , eval_module = @__MODULE__ )
5959
6060"""
@@ -90,13 +90,13 @@ Stiff parameters.
9090prob_ode_vanderpol_stiff = ODEProblem (van, [0 ; sqrt (3 )], (0.0 , 1.0 ), 1e6 )
9191
9292# ROBER
93- @parameters t k₁ k₂ k₃
93+ @parameters k₁ k₂ k₃
9494@variables y₁ (t) y₂ (t) y₃ (t)
95- D = Differential (t)
95+
9696eqs = [D (y₁) ~ - k₁ * y₁ + k₃ * y₂ * y₃,
9797 D (y₂) ~ k₁ * y₁ - k₂ * y₂^ 2 - k₃ * y₂ * y₃,
9898 D (y₃) ~ k₂ * y₂^ 2 ]
99- de = ODESystem (eqs; name = :rober )
99+ de = ODESystem (eqs,t ; name = :rober ) |> structural_simplify |> complete
100100rober = ODEFunction (de, [y₁, y₂, y₃], [k₁, k₂, k₃], jac = true , eval_module = @__MODULE__ )
101101
102102"""
@@ -171,13 +171,13 @@ prob_ode_threebody = ODEProblem(threebody,
171171
172172# Rigid Body Equations
173173
174- @parameters t I₁ I₂ I₃
174+ @parameters I₁ I₂ I₃
175175@variables y₁ (t) y₂ (t) y₃ (t)
176- D = Differential (t)
176+
177177eqs = [D (y₁) ~ I₁ * y₂ * y₃,
178178 D (y₂) ~ I₂ * y₁ * y₃,
179179 D (y₃) ~ I₃ * y₁ * y₂]
180- de = ODESystem (eqs; name = :rigid_body )
180+ de = ODESystem (eqs,t ; name = :rigid_body ) |> structural_simplify |> complete
181181rigid = ODEFunction (de, [y₁, y₂, y₃], [I₁, I₂, I₃], jac = true , eval_module = @__MODULE__ )
182182
183183"""
@@ -348,9 +348,9 @@ mm_f = ODEFunction(mm_linear; analytic = (u0, p, t) -> exp(inv(MM_linear) * mm_A
348348 mass_matrix = MM_linear)
349349prob_ode_mm_linear = ODEProblem (mm_f, rand (4 ), (0.0 , 1.0 ))
350350
351- @parameters t p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12
351+ @parameters p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12
352352@variables y1 (t) y2 (t) y3 (t) y4 (t) y5 (t) y6 (t) y7 (t) y8 (t)
353- D = Differential (t)
353+
354354eqs = [D (y1) ~ - p1 * y1 + p2 * y2 + p3 * y3 + p4,
355355 D (y2) ~ p1 * y1 - p5 * y2,
356356 D (y3) ~ - p6 * y3 + p2 * y4 + p7 * y5,
@@ -360,7 +360,7 @@ eqs = [D(y1) ~ -p1 * y1 + p2 * y2 + p3 * y3 + p4,
360360 p2 * y6 + p11 * y7,
361361 D (y7) ~ p10 * y6 * y8 - p12 * y7,
362362 D (y8) ~ - p10 * y6 * y8 + p12 * y7]
363- de = ODESystem (eqs; name = :hires )
363+ de = ODESystem (eqs,t ; name = :hires ) |> structural_simplify |> complete
364364hires = ODEFunction (de, [y1, y2, y3, y4, y5, y6, y7, y8],
365365 [p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12],
366366 jac = true )
@@ -396,13 +396,13 @@ prob_ode_hires = ODEProblem(hires, u0, (0.0, 321.8122),
396396 10.03 , 0.035 , 1.12 , 1.745 , 280.0 ,
397397 0.69 , 1.81 ))
398398
399- @parameters t p1 p2 p3
399+ @parameters p1 p2 p3
400400@variables y1 (t) y2 (t) y3 (t)
401- D = Differential (t)
401+
402402eqs = [D (y1) ~ p1 * (y2 + y1 * (1 - p2 * y1 - y2)),
403403 D (y2) ~ (y3 - (1 + y1) * y2) / p1,
404404 D (y3) ~ p3 * (y1 - y3)]
405- de = ODESystem (eqs; name = :orego )
405+ de = ODESystem (eqs,t ; name = :orego ) |> structural_simplify |> complete
406406jac = calculate_jacobian (de)
407407orego = ODEFunction (de, [y1, y2, y3], [p1, p2, p3], jac = true , eval_module = @__MODULE__ )
408408
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