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% matplotlib inline
#modified from 
#http://nbviewer.ipython.org/github/diogro/ode_examples/blob/master/The%20Fisher-Kolmogorov%20equation.ipynb?create=1
from numpy import *
from scipy.integrate import odeint
from matplotlib.pyplot import plot, xlabel, ylabel, figure, axes, style
style.use('ggplot')
#import time 
from timeit import default_timer as timer
import Fmodules 

ilciavo

#poisson solver
#u_xx = b(x)
%matplotlib inline 
from __future__ import division
import numpy as np
from numpy import cos, sin, zeros, pi
from numpy.linalg import solve, norm
import matplotlib.pyplot as plt
from matplotlib import rcParams
 

ilciavo

import matplotlib.pyplot as plt
from matplotlib import cm, colors
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d

class Arrow3D(FancyArrowPatch):
    def __init__(self, xs, ys, zs, *args, **kwargs):
        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)

ilciavo

%Modified from http://www.wikiwaves.org/Reaction-Diffusion_Systems
%Reaction Diffusion
% A + E -> 2A
% Differential Equations
% A_t = A_xx + A*E
% E_t = E_xx - E*A
% Equivalente to 
% A_t = A_xx + A*(1-A)

clc

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    %  Use of 2D FFT for Fourier-spectral solution of
    %
    %      ut = u_xx + u_yy 0 + u(1-u) , 0< x,y < 1
    %
    %  where
    % u0 = exp(-r^2/(2*sig^2)),  
    %      r^2 = (x-0.5)^2 + (y-0.5)^2, sig = 1
    %
    %  with periodic BCs on u in x,y, using N = 16 modes in each direction.
    %  Script makes a surface plot of u at the Fourier grid points.

ilciavo

%  Use of 2D FFT for Fourier-spectral solution of
%
%      ut = u_xx + u(1-u) , 0< x < 50
%
%  where
% u0 = exp(-r^2/(2*sig^2)),  
%      r^2 = (x-0.5)^2 , sig = 1
%
%  with periodic BCs on u in x,y, using N = 16 modes in each direction.
%  Script makes a surface plot of u at the Fourier grid points.