Hi friends

For One-Demensional wave equation (which is hyperbolic) and for One-Dimensional Inviscid Burger's eqn.(which is also hyperbolic eqn) Explicit schemes give good result or explicit schemes are the best bet.

Then can we make the statement like this " For hyperbolic eqn's explicit schemes are the best bet ?".If not the case in which cases they are ?

Thanks in advance.

regards rvndr

Implicit and explicit schemes refer to time discretization. Explicit schemes are restricted by the well-known CFL condition which puts an upper limit on the allowable time step dt. This means that you will have to perform more time steps to reach the desired solution. Explicit schemes have a more relaxed CFL condition which allows you to take larger time steps dt.

You could say: when the CFL condition is physically appropriate, explicit schemes are the best choice. However, for example for Euler equations, the shocks travel usually at the speed of the fluid, not at the speed of sound. In that case, the CFL condition is far too restrictive and implicit schemes are much better than explicit ones.

as i know the the CFL condition is taken at maximum wave speed u+c