You are right Y1:=w@Y can get the derivatives, but this is only one way to compute the derivatives. I want to obtain the derivatives by the built-in interpolant. Just recall maple return the solution for the other points (exceplt those nodes computed by RK45 method or whatever other methods) by interpolation. I think we can get the derivatives similar by interpolation. Only in this way, I can compute the residual, otherwise the residual is just zero. Thanks!

You are right Y1:=w@Y can get the derivatives, but this is only one way to compute the derivatives. I want to obtain the derivatives by the built-in interpolant. Just recall maple return the solution for the other points (exceplt those nodes computed by RK45 method or whatever other methods) by interpolation. I think we can get the derivatives similar by interpolation. Only in this way, I can compute the residual, otherwise the residual is just zero. Thanks!