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?
A program to simulate cellular automaton model
pde;ode;simulation;reference request;cellular automata
As @BlaisB mentioned, Mathematica has quite a bit of stuff built-in to do cellular automata. You might want to check that out if you have a license. I find Mathematica to be very nice when something has library functions you can use, but if you can't solve the problem by easily stringing together library functions then I find Mathematica much tougher to use than other languages.If you will need good performance, the ideal is to use Julia, C/C++, or FORTRAN. These days I would usually recommend Julia, but other scripting languages which can do this are Python, MATLAB, and even R.But what language you use really doesn't matter all that much (except for performance. There is a difference between the languages in terms of performance which might matter if your PDEs are difficult to solve).