Update ode_simple_nonlinear_prob.jl

Author: ChrisRackauckas

lib/ODEProblemLibrary/src/ode_simple_nonlinear_prob.jl

@@ -58,6 +58,16 @@ function vanderpol(du, u, p, t)
     du[2] = μ * ((1 - x^2) * y - x)
 end
 
+function vanderpol_jac(J, u, p, t)
+    x = u[1]
+    y = u[2]
+    μ = p[1]
+    J[1,1] = 0
+    J[2,1] = -2μ - 1
+    J[1,2] = 1
+    J[2,2] = μ * (1 - x^2)
+end
+
 """
 Van der Pol Equations
 
@@ -72,7 +82,8 @@ with ``μ=1.0`` and ``u_0=[\\sqrt{3}, 0]`` (where ``u[1] = x``, ``u[2] = y``)
 
 Non-stiff parameters.
 """
-prob_ode_vanderpol = ODEProblem(vanderpol, [sqrt(3), 0.0], (0.0, 1.0), [1.0])
+prob_ode_vanderpol = ODEProblem(ODEFunction(vanderpol, jac=vanderpol_jac), 
+    [sqrt(3), 0.0], (0.0, 1.0), [1.0])
 
 """
 Van der Pol Equations
@@ -435,4 +446,4 @@ where ``s=77.27``, ``w=0.161`` and ``q=8.375⋅10^{-6}``.
 Reference: [demoorego.pdf](http://www.radford.edu/~thompson/vodef90web/problems/demosnodislin/Demos_Pitagora/DemoOrego/demoorego.pdf)
 Notebook: [Orego.ipynb](http://nbviewer.jupyter.org/github/JuliaDiffEq/DiffEqBenchmarks.jl/blob/master/StiffODE/Orego.ipynb)
 """
-prob_ode_orego = ODEProblem(orego, [1.0, 2.0, 3.0], (0.0, 30.0), [77.27, 8.375e-6, 0.161])
+prob_ode_orego = ODEProblem(orego, [1.0, 2.0, 3.0], (0.0, 30.0), [77.27, 8.375e-6, 0.161])