root finding rounding error runge-kutta nd-order method runge-kutta-fehlberg sage (symbolic package) savetxt scalar ode scaling scheme script (and scripting) second-order ode rewritten as two first-order odes seed (random generators) simple pendulum simpson' rule simulation sir model source term spring damping of linear nonlinear oscillations spyder stability criterion stop program (ctrl+ ) str symbolic computations operations simplifications sympy syntax sys exit system of odes taylor series test block test function testing testing procedures text editor textwrangler theta rule title (plot) transpose (of matrix) trapezoidal rule tridiagonal matrix triple integral midpoint true try-exception tuple type conversion automatic unit tests unstable solutions validation variable assignment delete float global int local name str type vector vector ode vectorization verification verlet integration vim warning while loop wolframalpha write (to file) xlabel ylabel zeros index