upload solutions + typo fix

Author: FHoltorf

day_7/Chemical Reactions/exercises/Ex0/main.py

@@ -1,3 +1,3 @@
 import golden_module as gm
 
-print(gm.PHI)
+print("The golden ratio is given by (1+sqrt(5))/2 = " + str(gm.PHI))

day_7/Chemical Reactions/exercises/Ex3/runge_kutta.py

@@ -57,7 +57,7 @@ def integrate(f, x0, tspan, h, step):
         ts.append(t)
     return trajectory, ts
 
-def adaptive_explicit_RK_stepper(x,t,f,h,a,b,c,b_control):
+def adaptive_explicit_RK_stepper(f,x,t,h,a,b,c,b_control):
     """
         Implementation of generic explicit Runge-Kutta update for explicit ODEs
         

day_7/Chemical Reactions/presentation.pdf

@@ -0,0 +1 @@
+PHI = 1.618 # golden ratio

day_7/Chemical Reactions/solutions/Ex0/__init__.py

@@ -0,0 +1,3 @@
+import golden_module as gm
+
+print(gm.PHI)

day_7/Chemical Reactions/solutions/Ex0/golden_module.py

@@ -0,0 +1,9 @@
+a = [[1/5],
+     [3/40, 9/40], 
+     [44/45, -56/15, 32/9], 
+     [19372/6561, -25360/2187, 64448/6561, -212/729],  
+     [9017/3168, -355/33, 46732/5247, 49/176, -5103/18656], 
+     [35/384, 0, 500/1113, 125/192, -2187/6784, 11/84]]
+b = [35/384, 0, 500/1113, 125/192, -2187/6784, 11/84, 0]
+c = [0, 1/5, 3/10, 4/5, 8/9, 1, 1]
+b_control = [5179/57600, 0, 7571/16695, 393/640, -92097/339200, 187/2100, 1/40]

day_7/Chemical Reactions/solutions/Ex0/main.py

@@ -0,0 +1,52 @@
+# numpy for fast arrays and some linear algebra.
+import numpy as np 
+# import matplotlib for plotting
+import matplotlib.pyplot as plt
+# import Dormand-Prince Butcher tableau
+import dormand_prince as dp
+# import our Runge-Kutta integrators
+import runge_kutta as rk
+
+def dormand_prince_integrator(f, x, t, h):
+    return rk.explicit_RK_stepper(f, x, t, h, dp.a, dp.b, dp.c)
+    #return ... # please complete this function
+                # so it returns the prediction for the 
+                # Dormand-Prince method 
+                # To that end, use rk.explicit_rk_stepper!
+
+# Feel free play around with the following quantities 
+# and see how the solution changes!
+
+# time horizon
+tspan = (0.0,2.0)
+# time step 
+h = 0.2
+# initial condition
+x_0 = 3.0
+
+########################################
+### hereafter no more code modification necessary
+########################################
+
+# model right-hand-side
+def f(x,t):
+    return -2*x
+
+# simulate model 
+trajectory, time_points = rk.integrate(f, # ODE right-hand-side
+                                         x_0, # initial condition
+                                         tspan, # time horizon
+                                         h, # time step 
+                                         dormand_prince_integrator) # integrator
+
+# analytical solution
+time_points_analytical = np.linspace(tspan[0],tspan[1], 1000)
+trajectory_analytical = x_0*np.exp(-2*time_points_analytical)
+
+# plot trace
+fig, ax = plt.subplots()
+ax.set_xlabel("time")
+ax.set_ylabel("x(t)")
+ax.plot(time_points, trajectory, linewidth=2, color="red", marker="o")
+ax.plot(time_points_analytical, trajectory_analytical, linewidth=2, color="black", linestyle="dashed")
+fig.savefig("example_ode.pdf")