I'm an amateur in math. I have a system of nine PDE. The system is huge and I solve it numerically by an explicit finite difference scheme. The stencil I use:

One of PDE is a reaction-diffusion that creates a wave. It has a form:

\begin{align*} \frac{\partial}{\partial t}T(x,y,t)=D\Delta T(x,y,t) + R(T(x,y,t)) - F(T(x,y,t)) \end{align*}

$T(x,y,t)$ is the target function. $x,y$ are $2D$ space coordinates. $t$ is time. $R, F$ are reactions that depend on other PDE in the system.

Can I calculate how the wave of $T(x,y,t)$ is spreading? Its velocity and amplitude? I would be very grateful for a link to simple and clear materials about it.

Below is an example of waves spreading:


  • $\begingroup$ Are you working with plane waves? And what kind of velocity would you like to have? For example, there are the phase velocity: en.wikipedia.org/wiki/Phase_velocity and the group velocity: en.wikipedia.org/wiki/Group_velocity $\endgroup$ – Botond Jul 30 '18 at 19:02
  • $\begingroup$ @Botond Thank you for good questions. I work with 2d case. The wave is like a circle on the water surface. I've adjusted my post with a gif of it. Either of velocities will do fine for me. The one that is simpler to acquire is better. $\endgroup$ – vogdb Jul 30 '18 at 19:44
  • $\begingroup$ Is linearization an option? $\endgroup$ – Botond Jul 30 '18 at 20:01
  • $\begingroup$ I didn't understand about linearization. Linearization of what? Currently I'm solving numerically, so all functions calculations are linearised already. No? $\endgroup$ – vogdb Jul 31 '18 at 7:11

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