I understand that you want to solve first order pde in MATLAB.
Kindly refer to the following MATLAB Answer's that provide enough resources for getting started:
- https://www.mathworks.com/matlabcentral/answers/1595274-first-order-pde-system
- https://www.mathworks.com/matlabcentral/answers/502987-1d-pde-in-matlab-with-pdepe-first-order
I hope this helps!

