Hyperbolic equations 1

  • T/F: the second order wave equation is the same as a system of two first order wave equations.
  • What is the formula for the exact solution of the first order wave equation?
    • For an initially triangular profile, schetch the time/space evolution for the wave equation.
  • How do we find the MDE for the linear wave equation for a given discretization method?
  • If the leading truncation error term is second order, do you expect the method to be diffusive or dispersive?
  • If the leading truncation error term is third order, do you expect the method to be diffusive or dispersive?
  • Define $c$
  • What is the $c$ stability criteria for most of the methods?
  • Name the seven methods we discussed
    • What are the temporal and spatial orders for each?
    • Which are unconditionally unstable?
    • Which three can be recommended?