Week6: Wrap up: still the same error
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76
week6/ex1.py
76
week6/ex1.py
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@ -2,30 +2,23 @@
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import numpy as np
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def pdeHyperbolic(a, x, t, f, g = None, dtype=np.float64):
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def pdeHyperbolic(a, x, t, f, g, dtype=np.float64):
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""" Solve a Hyperbolic Partial Differential using finite differences. """
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m = len(x) # Amount of objects to track
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n = len(t) # Length of Time Vector
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# Determine stepsizes
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h = 1
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if m > 1:
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h = x[0] - x[1]
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k = 1
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if n > 1:
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k = t[0] - t[1]
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λ_sq = (a*k/h)**2
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# Create array to hold the solution
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w = np.zeros((n,m), dtype=dtype)
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# Create finite difference matrix
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A = np.diag(m*[2*(1 - λ_sq)], k=0) + np.diag((m-1)*[λ_sq], k=-1) + np.diag((m-1)*[λ_sq], k=1)
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print(A)
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# Initialise first two timesteps
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w[0] = f(x, t[0])
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@ -38,16 +31,13 @@ def pdeHyperbolic(a, x, t, f, g = None, dtype=np.float64):
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return w
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def test_pdeHyperbolic_case1(m=1e2, n=1e3,l=1, T=1):
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def test_pdeHyperbolic_case1(x_steps=1e2, t_steps=1e2, max_x=1, max_t=1):
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a = 1 # from the Schroedinger Equation
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# Setup spatial and time grids
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x = np.linspace(0, l, m)
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t = np.linspace(0, T, n)
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x = np.linspace(0, max_x, x_steps)
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t = np.linspace(0, max_t, t_steps)
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# Boundary conditions
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def f(x,t):
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@ -60,43 +50,18 @@ def test_pdeHyperbolic_case1(m=1e2, n=1e3,l=1, T=1):
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sol = pdeHyperbolic(a, x, t, f, g)
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# Plot it with the exact solution
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exact_sol = lambda x,t: np.sin(2*np.pi*x)*(np.cos(2*np.pi*t) + np.sin(2*np.pi*t))
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t_high_res = np.linspace(0, T, n * 1e4)
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exact_f = lambda x,t: np.sin(2*np.pi*x)*(np.cos(2*np.pi*t) + np.sin(2*np.pi*t))
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from matplotlib import pyplot
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from matplotlib import animation as anim
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fig, _ = pyplot.subplots()
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plot_animation(x, sol, func=exact_f)
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if False:
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for _, x_i in enumerate(x):
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pyplot.plot(t_high_res, exact_sol(x_i, t_high_res), label="Exact")
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pyplot.plot(t, sol[:,1], label="iter")
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pyplot.grid()
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pyplot.xlabel("t")
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pyplot.ylabel("w")
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else:
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def animate(i):
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pyplot.clf()
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pyplot.ylim(-2, 2)
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pyplot.grid()
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pyplot.plot(x, exact_sol(x, t[i]), label="exact")
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pyplot.plot(x, sol[i,:], label="iter")
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frames = np.arange(1, n, dtype=np.int)
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myAnim = anim.FuncAnimation(fig, animate, frames, interval = 10 )
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pyplot.legend()
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pyplot.show()
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def test_pdeHyperbolic_case2(m=200, n=400, l=1, T=1):
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def test_pdeHyperbolic_case2(x_steps=2e2, t_steps=4e2, max_x=1, max_t=1):
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a = 1 # from the Schroedinger Equation
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# Setup spatial and time grids
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x = np.linspace(0, l, m)
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t = np.linspace(0, T, n)
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x = np.linspace(0, max_x, x_steps)
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t = np.linspace(0, max_t, t_steps)
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# Boundary conditions
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def f(x,t):
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@ -108,6 +73,11 @@ def test_pdeHyperbolic_case2(m=200, n=400, l=1, T=1):
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# Solve it
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sol = pdeHyperbolic(a, x, t, f, g)
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plot_animation(x, sol)
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def plot_animation(x, sol, func=None, interval = 10):
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from matplotlib import pyplot
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from matplotlib import animation as anim
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fig, _ = pyplot.subplots()
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@ -115,17 +85,25 @@ def test_pdeHyperbolic_case2(m=200, n=400, l=1, T=1):
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def animate(i):
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pyplot.clf()
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pyplot.grid()
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pyplot.ylim(-1.5,1.5)
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pyplot.ylim(-1.5, 1.5)
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pyplot.title('t = {}/{}'.format(i, len(sol)))
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#if func is not None:
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# pyplot.plot(x, func(x, sol[i]), label='exact')
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pyplot.plot(x, sol[i,:], label="iter")
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frames = np.arange(1, n)
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myAnim = anim.FuncAnimation(fig, animate, frames, interval = 5 )
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frames = np.arange(0, len(sol))
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try:
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myAnim = anim.FuncAnimation(fig, animate, frames, interval = interval )
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pyplot.legend()
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pyplot.show()
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except AttributeError:
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# This final error is fugly
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pass
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if __name__ == "__main__":
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#test_pdeHyperbolic_case1()
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test_pdeHyperbolic_case2()
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test_pdeHyperbolic_case1()
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#test_pdeHyperbolic_case2()
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