I have worked on mathematical modeling based on differential equations, and now I want to simulate a cellular automaton based on a system of mixed ode-pde coupled first order differential equations
\begin{eqnarray}
\dfrac{dR}{dt}(t)&=&v_r(R,t),\\
\dfrac{\partial v_r}{\partial r}(r,t)&=&\dfrac{R\sinh(r)}{r\sinh(R)}[1-\zeta_1\sqrt{\sigma_r^2(r,t)+2(\sigma_r(r,t)-\beta(r,t))^2}]-\epsilon[1+\zeta_2\sqrt{\sigma_r^2(r,t)+2(\sigma_r(r,t)-\beta(r,t))^2}]-2\dfrac{v_r(r,t)}{r},\\
\dfrac{\partial\sigma_r}{\partial r}(r,t)&=&-\dfrac{2\beta}{r},\\
\gamma(r,t)&=&\left(\dfrac{\partial}{\partial t}+v_r(r,t)\dfrac{\partial}{\partial r}\right)\beta(r,t),\end{eqnarray}
where $\gamma$ is a given function depending also of $R,\;\sigma_r,\;v_r,\;\beta$ corresponding to a model with domain $\Omega\subset\mathbb{R}^2$ compact (and of course with the necessary initial and boundary conditions). But I am new in this and I have no idea of a programming platform or software (I'm not really sure how to say that) to achieve my goal.
Can anyone recommend a good program to simulate cellular automaton?
