Are higher order radiation boundary conditions more accurate?

Radiation boundary conditions are used to terminate the computational region in a differential-equation-based calculation of electromagnetic fields. Rigorous mathematical results describe the order of accuracy of several of these approximations as the boundary is moved towards infinity (for a fixed region containing the scatterer and/or sources). Practical interest centers on their use as close as possible to the scatterer and/for sources. Although increasing the order of the boundary conditions can generally be proven to increase accuracy when applied near infinity, some examples are given illustrating that the opposite may be true close in. Thus, one cannot always simply go to higher order boundary conditions to obtain accurate results.<>