(c) (Optional) Calculate the fo/2 Padé approximant to e, where θ is rea I. Show that the leading-order error is θ3/...
(c) (Optional) Calculate the fo/2 Padé approximant to e, where θ is rea I. Show that the leading-order error is θ3/6 Consider Eq. (1), with U = 0 at x = 0 and x 1, approximated at the mesh points xm-Tnh, mに1 N-1, Nh = 1, along the time level tn nk by the set of difference equations and λ = k/h2, and TN-1 is the matrix of order N-1 repre- senting the second order operator 62 Investigate the stability of the difference scheme. iii. Also, could discontinuities between boundary conditions and ini- tial values possibly induce finite oscillations in the numerical solution?
(c) (Optional) Calculate the fo/2 Padé approximant to e, where θ is rea I. Show that the leading-order error is θ3/6 Consider Eq. (1), with U = 0 at x = 0 and x 1, approximated at the mesh points xm-Tnh, mに1 N-1, Nh = 1, along the time level tn nk by the set of difference equations and λ = k/h2, and TN-1 is the matrix of order N-1 repre- senting the second order operator 62 Investigate the stability of the difference scheme. iii. Also, could discontinuities between boundary conditions and ini- tial values possibly induce finite oscillations in the numerical solution?