Numerical methods for nonlinear wave equation

Question

What would be the best numerical method to solve nonlinear wave equation aka

$u_{tt}-u_{xx}=f(u)$ with initial and boundary conditions $u(x,0) = \phi(x)$, $u_{t}(x, 0) = 0$

Actually any information would be helpful...

Answer 1

What mathematical software tools do you have available? It usually doesn't pay to reinvent the wheel. In Maple you could do something like this:

pde:= diff(u(x,t),t,t) = diff(u(x,t),x,x) + u(x,t)^2;

ibc:= {u(0,t) = 1, D[2](u)(x,0) = 0, u(x,0)=1,u(1,t) = 1};

solution:= pdsolve(pde,ibc, numeric,time=t,range = 0..1);