I am reading this paper and came across a system of differential equations with 4 ODEs and 1 PDE. The PDE is given below. My question is how to solve this numerically in MATLAB , Python or Mathematica?
Here $\tau$ is time, $x$ is a generic point in the plane, subscript $i$ designates the $i$th biological amoeba cell, whose position in the plane is denoted $x_i$, $w_5$ is a extracellular biochemical concentration (cAMP) generated by amoeba, $sr({w_4}^i)$ is the secretion rate function dependent on $w_4$ which is intracellular cAMP concentration, $\Delta_1$ is the diffusion constant, $\delta(.)$ is the delta function, $\nabla^2(w_5(x))$ is the laplacian, others constants.
There are packages available for MATLAB do solve partial differential equations (e.g., Partial Differential Equation Toolbox) but I believe they are add-ons that you have to pay for.