fix: RK

numeric.py

@@ -3,7 +3,7 @@ import matplotlib.pyplot as plt
 
 threshold = 100
 
-def RK_n(y0, t: np.ndarray, n=4):
+def RK4(y0, t):
     ODE = lambda t, y: t**3 + y**3
     #note: t is a vector of time points, y0 is the initial value
     steps = len(t)
@@ -16,17 +16,13 @@ def RK_n(y0, t: np.ndarray, n=4):
     t0_idx = np.where(t >= 0)[0][0]
     y[t0_idx] = y0  # set the initial condition at t[0]
     
-    #forward RK
     for i in range(t0_idx, steps - 1):
-        #n-th order Runge-Kutta method
-        k = np.zeros(n)
-        k[0] = h * ODE(t[i], y[i])
-        for j in range(1, n):
-            t_j = t[i] + h * (j / n)
-            y_j = y[i] + k[j - 1] / n
-            k[j] = h * ODE(t_j, y_j)
-        y[i + 1] = y[i] + np.sum(k) / n
-    return y
+        k1 = h * ODE(t[i], y[i])
+        k2 = h * ODE(t[i] + h / 2, y[i] + k1 / 2)
+        k3 = h * ODE(t[i] + h / 2, y[i] + k2 / 2)
+        k4 = h * ODE(t[i] + h, y[i] + k3)
+        y[i + 1] = y[i] + (k1 + 2 * k2 + 2 * k3 + k4) / 6
+    return y    
 
 def euler(f, a, b, y0, h):
     xs = [a]
@@ -84,7 +80,7 @@ for idx, (y0, xm, xM, ym, yM) in enumerate(lims):
         Te, Ye = euler(ODE, 0, xM, y0, h)
         Ti, Yi = improvedEuler(ODE, 0, xM, y0, h)
         Tr = np.linspace(0, xM, int((xM - 0)/h))
-        Yr = RK_n(y0, Tr)
+        Yr = RK4(y0, Tr)
         
         axes[idx][0].plot(Te, Ye, label=f'$\Delta t$={h}', linewidth=1)
         axes[idx][1].plot(Ti, Yi, label=f'$\Delta t$={h}', linewidth=1)