Wave Equation Amplication Issue

When I try to use the wave equation the amplitude of the wave is amplified by a lot over the duration of the simulation. Here is my code:

import numpy as np
from pde import FieldCollection
from pde import (DiffusionPDE, UnitGrid, ScalarField, MemoryStorage,
                 PlotTracker, PrintTracker, RealtimeIntervals, DataTracker)
from pde.visualization import movies
import math
import random
import pde
import pandas
import ffmpeg
import matplotlib.pyplot as plt; plt.rcdefaults()
import numpy as np
import matplotlib.pyplot as plt


storage = MemoryStorage()

trackers = [
    'progress',                    # show progress bar during simulation
    'steady_state',                # abort when steady state is reached
    storage.tracker(interval=1),   # store data every simulation time unit
    PlotTracker(show=True),        # show images during simulation
]

grid = pde.UnitGrid([64, 64])
field1 = ScalarField.random_uniform(grid, 0, 0)  # generate initial condition
field2 = ScalarField(grid);
field1.add_interpolated([48, 48], 1)
field1.add_interpolated([48,16], 1)
state = FieldCollection([field1,field2]); #first slot is the density field, 

eq = pde.WavePDE(speed=1);
result = eq.solve(state, t_range=200, dt=1, tracker = trackers)
result.plot(colorbar = True, show = True)       # plot the resulting field
movies.movie_multiple(storage, filename = r'C:\Users\matth\URECA Simulation\testfile.mp4')

and here is the file of the movie. In the movie the colorbar is at 10^90 and the wave can only be seen at the end of the movie, which means that the amplitude is increasing throughout the simulation. I looked at the documentation and I am not sure why this is happening.

[david-zwicker]

I’m not an expert on these methods but I would certainly welcome pull requests that implement more general solvers. A good starting point would probably be to look at the implementations of pde.solvers.implicit and pde.solvers.explicit. I just realized that the explicit solver already supports Runge-Kutta 4/5, which is an explicit stepper. It would be great to have more methods available, either as extensions to the present solver classes or as a separate RungeKuttaSolver class.

[MatthewBelzer]

I just reduced dt to .0001. I don’t think using the implicit and explicit methods changed it that much.