I am a physicist by trade, but I as this is a pure maths question I thought I'd ask it here.
I need to solve the following PDE for a project:
$$\frac{\partial^2 P}{\partial t^2} + \beta \frac{\partial P}{\partial t} = a \Big(\frac{\partial^2 P}{\partial x^2} - \frac{\partial^2 P}{\partial y^2} \Big) + b - \sin(P), $$ where $\beta$, $a$ and $b$ are all constants. I am trying to numerically solve this PDE over a rectangular domain, with $x$ running from $0$ to $W$ and $y$ running from $0$ to $L$. I am unsure where to begin, after first looking into MATLAB's PDE toolbox, I found that it can only solve PDEs that fit into the categories of elliptic, parabolic, hyperbolic or eigenmodes, which I believe this equation does not. The conditions at the boundaries are given by the Dirichlet condition $P = 0$ and the Neumann condition $\nabla P = 0$.
My main question is, are there any software platforms on which I could solve this PDE numerically?
Thanks for any suggestions!