Error structure of conservative 4-point finite-difference scheme on non-uniform meshes

We investigate accuracy of finite-difference scheme R3 based on conservative 4-point derivative approximation on non-uniform meshes, in application to model problem $u'+\lambda u=0$, $u(0)=1$. It is shown that the relative error consists of three parts: the first one does not accumulate while going away from the boundary of the computational domain, the second one is proportional to the square of the maximal difference of adjacent mesh steps, and the third one is of the third order with respect to the maximal mesh step. Thus despite the second order of accuracy on large computational domains and not too rough meshes R3 scheme behaves like third order schemes.