CD1Upwind[\[Phi]_, \[Psi]_, f_, c_, n_, m_, x0_, x1_, t0_] :=
 Module[{dt = t0/n, dx = (x1 - x0)/m, u = {}},
  AppendTo[u, Table[\[Phi][x0 + dx*i], {i, 0, m}]];
  For[i = 1, i <= n, ++i,
   AppendTo[u, {\[Psi][t0 + dt*i]}];
   For[j = 2, j <= m + 1, ++j,
    AppendTo[u[[i + 1]],
      u[[i]][[j]] - (c*dt)/
        dx (u[[i]][[j]] - u[[i]][[j - 1]] +
          f[x0 + dx*(j - 1), t0 + dt*i])];
    ]
   ];
  Table[Table[{x0 + dx*i, u[[j]][[i + 1]]}, {i, 0, m}], {j, Length[u]}]
  ]