No, it will not work well without the optimal method. But the method is no longer optimal if say a nonlinear term is added to these equations, so you can use th

No, it will not work well without the optimal method. But the method is no longer optimal if say a nonlinear term is added to these equations, so you can use the "optimal" method as a starting point and then try to nudge towards something better. Don't throw away any information that you have.