Page - 173 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

5.1 FiniteDifferenceMethods 173 Fig.5.3 Snapshots of thedimensionless solutionofa scaledproblem rhs[1:N-1] = (beta/dx**2)*(u[2:N+1] - 2*u[1:N] + u[0:N-1]) + g(x[1:N], t) This rewrite speedsup thecodebyabout a factor of 10. Acomplete code is found in thefilerod_FE_vec.py. 5.1.6 UsingOdespytoSolvetheSystemofODEs LetusnowshowhowtoapplyageneralODEpackagelikeOdespy(seeSect.4.3.6) to solveourdiffusionproblem.As longaswehavedefineda right-handside func- tionrhs this isverystraightforward: import odespy solver = odespy.RKFehlberg(rhs) solver.set_initial_condition(U_0) T = 1.2 N_t = int(round(T/float(dt))) time_points = linspace(0, T, N_t+1) u, t = solver.solve(time_points)