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?