MATLAB: Can I solve the first-order partial differential equation with PDEPE function in MATLAB 7.6 (R2008a)

MATLABpde

I have a first order PDE that I am want to solve:
 du/dt+du/dx+u=0,
 u(x,0)=exp(-x)
However, when I try solving this equation with PDEPE function I get an error:
 ??? Error using ==> daeic12 at 77
 This DAE appears to be of index greater than 1.
 Error in ==> ode15s at 395
     [y,yp,f0,dfdy,nFE,nPD,Jfac] = daeic12(odeFcn,odeArgs,t,ICtype,Mt,y,yp0,f0,...
 Error in ==> pdepe at 320
   [t,y] = ode15s(@pdeodes,t,y0,opts);
 Error in ==> modified at 17
 sol = pdepe(m,@ppde,@pic,@pbc,x,t);

Best Answer

The ability to solve the first-order PDE with PDEPE function is not available in MATLAB 7.6 (R2008a).
PDEPE function can only solve parabolic-elliptic PDEs in 1D.
You can use method of separation of variables or method of characteristics to solve this equation analytically.
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