  This paper introduces a fast and numerically stable algorithm for the
solution of fourth-order linear boundary value problems on an interval. This
type of equation arises in a variety of settings in physics and signal
processing. Our method reformulates the equation as a collection of second-kind
integral equations defined on local subdomains. Each such equation can be
stably discretized and solved. The boundary values of these local solutions are
matched by solving a banded linear system. The method of deferred corrections
is then used to increase the accuracy of the scheme. Deferred corrections
requires applying the integral operator to a function on the entire domain, for
which we provide an algorithm with linear cost. We illustrate the performance
of our method on several numerical examples.
