> Normally I can differentiate analytically to get the slope and > inflection points. While trying to have a quick look into these points > with numerical differentiation I noticed that mpmath is giving me > values quite distant from the ones obtained with analytical formulas.
I think there's a missing term in your analytical derivatives. Your three functions are # fundamental mode def phi(x): return mpmath.cos(k*x) - mpmath.cosh(k*x) + alpha* ( mpmath.sin(k*x) - mpmath.sinh(k*x) ) # slope of fundamental def phi_dx(x): return -mpmath.sin(k*x) - mpmath.sinh(k*x) + alpha* ( mpmath.cos(k*x) - mpmath.cosh(k*x) ) # curvature of fundamental def phi_dx2(x): return -mpmath.cos(k*x) - mpmath.cosh(k*x) - alpha* ( mpmath.sin(k*x) + mpmath.sinh(k*x) ) and it looks to me like you're missing a factor of k in phi_dx and k^2 in phi_dx2. Inserting them seems to get rid of the discrepancy. Doug -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
