It seems like leapfrog is defined for the 2nd order PDE wave equation. For a 1st order formulation like the velocity-stress formulation, is there a way to use the leapfrog integration? The reason I ask is that leapfrog is more stable than other some other integrator like RK4. Thanks!
Hi Bo, leapfrog scheme for a 1st order formulation is what is usually being referred to as Central difference: df/dt \approx (f(n+1) - f(n-1))/2dt
Hi Bo,
as Matej said, there usually should be no problems using the leapfrog method. But you should apply the ,,one-way leapfrog'' method, i.e. for the equation
u_t - c u_x = 0
the leapfrog would be
u(j,n+1) - u(j,n-1) = c \delta t / \delta x ( u(j+1,n) - u(j-1, n) ).
Then you are integrating with respect to position and time.
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