#!/usr/bin/env python # -*- coding: utf-8 -*- # Copyright (C) 2010 Modelon AB # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as published by # the Free Software Foundation, version 3 of the License. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU Lesser General Public License for more details. # # You should have received a copy of the GNU Lesser General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import numpy as N import nose from assimulo.solvers import RungeKutta4 from assimulo.problem import Explicit_Problem def run_example(with_plots=True): r""" Demonstration of the use of the use of Runge-Kutta 4 by solving the linear test equation :math:`\dot y = - y` on return: - :dfn:`exp_mod` problem instance - :dfn:`exp_sim` solver instance """ #Defines the rhs def f(t,y): ydot = -y[0] return N.array([ydot]) #Define an Assimulo problem exp_mod = Explicit_Problem(f, 4.0, name = 'RK4 Example: $\dot y = - y$') exp_sim = RungeKutta4(exp_mod) #Create a RungeKutta4 solver #Simulate t, y = exp_sim.simulate(5, 100) #Simulate 5 seconds #Basic test nose.tools.assert_almost_equal(float(y[-1]),0.02695179) #Plot if with_plots: import pylab as P P.plot(t, y) P.title(exp_mod.name) P.ylabel('y') P.xlabel('Time') P.show() return exp_mod, exp_sim if __name__=='__main__': mod,sim = run_example()