I want to do the numerical simulations in MATLAB for the following partial delay differential equations with Dirichlet boundary condition. I need to know the simplest method to do that. \begin{equation} \left\{ \begin{aligned} \frac{\partial ^{2}z}{\partial t^{2}}\left( x,t\right) &=\frac{\partial ^{2}z}{\partial x^{2}}\left( x,t\right) +v\left( t\right) \frac{\partial z}{\partial t}\left( x,t-r\right) , & t&\geq 0,~~ x\in \Omega \\ z\left(x,\theta\right)&=\sin\left(x\theta\right) , &\theta&\in \left[ -r,0\right] & \end{aligned} \right. \end{equation}
Here r denoting the delay is a positive real number, and $\Omega =\left( 0,1\right) $ .
N.B: Thank you for your help