#########################################################################################

##

## PathSim stiff flame ODE example

##

#########################################################################################

# IMPORTS ===============================================================================

import numpy as np

import matplotlib.pyplot as plt

from pathsim import Simulation, Connection

from pathsim.blocks import Scope, Integrator, Adder, Function

from pathsim.solvers import ESDIRK32, ESDIRK43, GEAR52A

# FLAME INITIAL VALUE PROBLEM ===========================================================

#flame parameter (very stiff)

delta = 0.0001

#blocks that define the system

Int = Integrator(delta)

Fnc = Function(lambda x: x**2 - x**3)

Sco = Scope()

blocks = [Int, Fnc, Sco]

#the connections between the blocks

connections = [

Connection(Int, Fnc, Sco),

Connection(Fnc, Int)

]

#initialize simulation with the blocks, connections, timestep and logging enabled

Sim = Simulation(

blocks,

connections,

dt=0.1,

Solver=ESDIRK43,

tolerance_lte_abs=1e-6,

tolerance_lte_rel=1e-4

)

# Run Example ===========================================================================

if __name__ == "__main__":

Sim.run(2/delta)

#plotting

Sco.plot(".-")

plt.show()