I have two coupled differential equations as follows \begin{eqnarray} \frac{\partial }{\partial x}U(x,y)&=&2V(x,y), \notag \ \frac{\partial }{\partial y}V(x,y) &=&V(x,y)U(x,y)+1, \end{eqnarray} with initial conditions \begin{equation} U(0,y)=\sin (y)\,,\qquad V(x,0)=0, \end{equation} To solve the above equations with the NDSolve command in Mathematica, the following errors are obtained

NDSolve[{D[U[x, y], x] == 2 V[x, y], D[V[x, y], y] == V[x, y] U[x, y] + 1, V[x, 0] == 0, U[0, y] == Sin[y]}, {U, V}, {x, 0, 2}, {y, 0, 2}]
NDSolve`FEM`InitializePDECoefficients::femcscd: The PDE is convection dominated and the result may not be stable. Adding artificial diffusion may help.
FindRoot::stfail: The method AffineCovariantNewton failed to compute the next step.
FindRoot::sszero: The step size in the search has become less than the tolerance prescribed by the PrecisionGoal option, but the function value is still greater than the tolerance prescribed by the AccuracyGoal option.

Please help me with this.