Numerical Treatment of Potential Type Equations on $\mathbb{R}^n $: Theoretical Considerations

This article discusses the numerical treatment on $\mathbb{R} ^n (n \geqq 3)$ of the form $\nabla \cdot (A\nabla u) - Pu = f$ where $A$ approaches the identity at infinity and $f$ and $P$ vanish sufficiently rapidly at infinity. In particular, the error introduced by using a finite artificial radius is studied when various boundary conditions are used. It is shown that the use of higher order boundary conditions greatly reduces the error introduced by employing an artificial radius.