SciPy Recipes

How it works...

We compute each step sequentially and compare it to the actual solution, which is known. You will notice that there is virtually no difference:

import numpyfrom scipy.integrate import odef=lambda t,y: -20*y # The ODEactual_solution=lambda t:numpy.exp(-20*t) # actual solutiondt=0.01 # time stepsolver=ode(f).set_integrator('dop853') # solversolver.set_initial_value(1,0) # initial valuewhile solver.successful() and solver.t<=1+dt:   # solve the equation at successive time steps,   # until the time is greater than 1   # but make sure that the solution is successful       print (solver.t, solver.y, actual_solution(solver.t))   # We compare each numerical solution with the actual   # solution of the ODE solver.integrate(solver.t + dt) # solve next ...