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% Equation FKPP difference finie 1D implicite Crank-Nicolson
% FKPP equation with finite-difference implicite Crank-Nicolson

% parametre des equations/equation parameters
r = 0.5; % taux de croissance/growth rate
D = 0.1; % coefficient de diffusion/diffusion coefficient

% parametres de simulation, espace/space simulation parameters
% x in domain Omega = [x0,x1]
h = 0.05;  % intervalle de discretisation spatiale/space step

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% Equation FKPP difference finie 1D explicite
% FKPP equation with explicit finite difference scheme

% parametre des equations
% equation parameters
r = 0.5;        % taux de croissance/growth rate
D = 0.1;        % coefficient de diffusion/diffusion coefficient

% parametres d'espace
% space parameters

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function sol = kuramoto
% KURAMOTO Systeme d'oscillateurs de phase couples
%   sol = kuramoto resoud un systeme de N d'oscillateurs de phase couples

% intervalle d'integration
t0 = 0;
tfinal = 500;

% nombre d'oscillateurs
N = 400;

samubernard

%% Turing Patterns in 2D: an example with the FitzHugh-Nagumo equations 

% parametre des equations
% equation parameters
epsilon = 0.08;
b = 0.7;
c = 0.8;
Dv = 0.1;
Dw = 1.6; 
I = 0.35;

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function [c,f,s] = turing(x,t,u,DuDx)
% TURING PDE components for the Turing equations
%
%   Examples
%       x = -20:0.1:20;
%       t = 0:20;
%       sol = pdepe(0,@turing,@turingic,@turingbc,x,t);
%       u = sol(:,:,1);
%       v = sol(:,:,2);
%       imagesc(x,t,u); axis xy;

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%% FitzHugh-Nagumo avec diffusion 1D
% 1D FitzHugh-Nagumo with diffusion

% parametre des equations
% equation parameters
epsilon = 0.08;
b = 0.7;
c = 0.8;
D = .01;        % coefficient de diffusion/diffusion coefficient
I = 0.0;

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# coding: utf-8

## Méthode de la puissance pour le calcul de valeurs propres

# In[1]:

from numpy import *
import matplotlib as plt
import pylab as pl