What do you do to handle the boundaries (-1 and +1) of the spatial domain? How large are the timesteps that can be used? What is the order of accuracy of the procedure? The wave equation in one spatial dimension.
Write a code which uses 3 time levels to explicitly evolve the wave equation
(d^2/dx^2)Q - (d^2/dt^2)Q = 0.
The discretization should be on the coordinate interval (-1, 1) with at least 200 spatial grid points. Data should be set so that the initial (t=0) value of Q is nonzero in (-.2, .2) and is zero outside this interval. Set the initial time derivative of Q to be zero.
Questions:
What do you do to handle the boundaries (-1 and +1) of the spatial domain?
How large are the timesteps that can be used?
What is the order of accuracy of the procedure?