DiffEq Solutions

Solution to the Lorenz Problem


In [1]:
using DifferentialEquations

f = @ode_def_nohes LorenzExample begin
  dx = σ*(y-x)
  dy = x*(ρ-z) - y
  dz = x*y - β*z
end σ ρ β

u0 = big.([0.1;0.0;0.0])
tspan = (big(0.0),big(100.0))
prob = ODEProblem(f,u0,tspan,(10.0,28.0,2.6666))
sol = solve(prob);

In [2]:
using Plots; gr(); plot(sol)


Out[2]:
0 20 40 60 80 100 -20 0 20 40 t x(t) y(t) z(t)

In [3]:
plot(sol,vars=(:x,:y,:z))


Out[3]:
x y (x,y,z)

Solution to the Ball Bounce Problem


In [5]:
f = function (du,u,p,t)
  du[1] = u[2]
  du[2] = -9.81
end

condtion = function (u,t,integrator) # Event when event_f(t,u,k) == 0
  u[1]
end

affect! = nothing
affect_neg! = function (integrator)
  integrator.u[2] = -0.8integrator.u[2]
end

callback = ContinuousCallback(condtion,affect!,affect_neg!,interp_points=100)

u0 = [50.0,0.0]
tspan = (0.0,15.0)
prob = ODEProblem(f,u0,tspan)


sol = solve(prob,Tsit5(),callback=callback,adaptive=false,dt=1/4)
plot(sol)


Out[5]:
0 5 10 15 -20 0 20 40 t u1(t) u2(t)