using NeuralNetDiffEq
using Base.Test
using Plots; plotly()
using DiffEqBase, ParameterizedFunctions
using DiffEqProblemLibrary, DiffEqDevTools
using Knet

linear = (t,u) -> (1.01*u)
(f::typeof(linear))(::Type{Val{:analytic}},t,u0) = u0*exp(1.01*t)
prob = ODEProblem(linear,1/2,(0.0,1.0))
sol = solve(prob,nnode(10),dt=1/10,iterations=10)
#dts = 1./2.^(8:-1:2)
#sim_linear  = test_convergence(dts,prob,nnode(10),iterations=5000)

plot(sol,plot_analytic=true)

sol(0.232)

f = (t,u) -> (t^3 + 2*t + (t^2)*((1+3*(t^2))/(1+t+(t^3))) - u*(t + ((1+3*(t^2))/(1+t+t^3))))
(::typeof(f))(::Type{Val{:analytic}},t,u0) =  u0*exp(-(t^2)/2)/(1+t+t^3) + t^2
prob2 = ODEProblem(f,1.0,(0.0,1.0))
sol2 = solve(prob2,nnode(10),dt=0.1,iterations=200)

plot(sol2,plot_analytic=true)



f2 = (t,u) -> (-u/5 + exp(-t/5).*cos(t))
(::typeof(f2))(::Type{Val{:analytic}},t,u0) =  exp(-t/5)*(u0 + sin(t))
prob3 = ODEProblem(f2,Float32(0.0),(Float32(0.0),Float32(2.0)))
sol3 = solve(prob3,nnode(10),dt=0.2,iterations=1000)

plot(sol3,plot_analytic=true)

sol3([0.721])

f4 = (t,u) -> (u - t)
(::typeof(f4))(::Type{Val{:analytic}},t,u0) =  (t+1) - (1/3)*(e^t)
prob4 = ODEProblem(f4,Float32(2/3),(Float32(0.0),Float32(2.0)))
sol4 = solve(prob4,nnode(10),dt=0.2,iterations=1000)

plot(sol4, plot_analytic=true)

sol4(1)

f5 = (t,u) -> ((1/t)*(2-u))
(::typeof(f5))(::Type{Val{:analytic}},t,u0) =  2/t + 2
prob5 = ODEProblem(f5,Float32(4),(Float32(1.0),Float32(4.0)))
sol5 = solve(prob5,nnode(10),dt=0.3,iterations=1000)

plot(sol5, plot_analytic=true)

f6 = (t,u) -> 2*sin(3t) + u/2
(::typeof(f6))(::Type{Val{:analytic}},t,u0) = (((-4/37)*e^(-t/2)*(6*cos(3t)+sin(3t)))/(e^(-t/2))) 
prob6 = ODEProblem(f6,Float32(24/37),(Float32(pi/3),Float32(2*pi/3)))
sol6 = solve(prob6,nnode(10),dt=Float32(pi)/30,iterations=1000)

plot(sol6, plot_analytic = true)