  The aim of this paper is to study jumping numbers and multiplier ideals of
any ideal in a two-dimensional local ring with a rational singularity. In
particular we reveal which information encoded in a multiplier ideal determines
the next jumping number. This leads to an algorithm to compute sequentially the
jumping numbers and the whole chain of multiplier ideals in any desired range.
As a consequence of our method we develop the notion of jumping divisor that
allows to describe the jump between two consecutive multiplier ideals. In
particular we find a unique minimal jumping divisor that is studied
extensively.

Algebraic Geometry;Commutative Algebra