Use 'matlabFunction' to create a numerical equivalent of the symbolic expressions. Refer to this link
For example:
matlabFunction(u, u_z, dt,'file','sysEqn')
Will create 'sysEqn.m' that gives the numerical values of u, u_z, dt. You can parameterize the resulting function by making sure any parameters are defined as 'syms' in the original symbolic code.