to solve some partial differential equations by using matlab, you can use the Partial Differential Equation Toolbox. It is very easy to implement and is going to give you great numerical approximations. Here I attach the link:
" Solutions of first order partial differential equations–f(p, q)=0,
f(z, p, q)=0, f(x, p)=F(y, q) and Clauirat’s - Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients. "
For example, state dependent delays, time dependent delay and, for example, differential equations with piecewise constant arguments (delayed and advanced argument) are not solvable there...you have to write a script in order to try to solve it by steps... (if you can to represent or write the solution in a proper and convenient way)...
there is no packages for this type of equations yet... hard work.,..line by line of code...
Theoretically Yes! you can attack ant PDE system in Matlab toolbox. , But Convergence is strongly dependent on the problem type. Soe problems, such as semiconductor equations are very stiff and the dynamic range of variables is horrible! Therefore such problems need special techniques,which may not be available in Matlab toolbox