Hi, for a second-order time dependent PDE, like
\frac{\partial^2 u}{\partial t^2}=L(u)
Centered difference approximation for time is
\frac{u^{n+1}-2u+u^{n-1}}{\Delta t^2}
Backward difference approximation for time is
\frac{2u^{n}-5n^{n-1}+4n^{n-2}-u^{n-3}}{\Delta t^2}
Forward difference approximation for time is
\frac{2u^{n}-5n^{n+1}+4n^{n+2}-u^{n+3}}{\Delta t^2}
I am confused, what are the unknowns in these methods?
For example, in the Centered difference method, is u^{n+1} the unknown or u^{n} is the unknown in the current timestep n?
Formulas are from