Page - 133 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

4.3 OscillatingOne-DimensionalSystems 133 Fig.4.21 Simulationof10periodsofoscillationsbyHeun’smethod import odespy def f(u, t): return u method = odespy.Heun # or, e.g., odespy.ForwardEuler solver = method(f) solver.set_initial_condition(2) time_points = np.linspace(0, 4, 101) u, t = solver.solve(time_points) In other words, you define your right-hand side function f(u, t), initialize an Odespysolverobject, set the initialcondition,computeacollectionof timepoints whereyouwant the solution, andask for the solution. The returnedarraysu andt canbeplotteddirectly:plot(t, u). A nice feature of Odespy is that problem parameters can be arguments to the user’sf(u, t) function. Forexample, ifourODEproblemisu0 D auCb,with twoproblemparametersa andb,wemaywriteourf functionas def f(u, t, a, b): return -a*u + b Theextra,problem-dependentargumentsaandbcanbe transferred to this function ifwecollect their values in a list or tuplewhencreating theOdespy solver anduse thef_argsargument: