  In [Proc. Roy. Soc. London Ser. A 453 (1997), no. 1962, 1411-1443] A.S. Fokas
introduced a novel method for solving a large class of boundary value problems
associated with evolution equations. This approach relies on the construction
of a so-called global relation: an integral expression that couples initial and
boundary data. The global relation can be found by constructing a differential
form dependent on some spectral parameter, that is closed on the condition that
a given partial differential equation is satisfied. Such a differential form is
said to be fundamental [Quart. J. Mech. Appl. Math. 55 (2002), 457-479]. We
give an algorithmic approach in constructing a fundamental k-form associated
with a given boundary value problem, and address issues of uniqueness. Also, we
extend a result of Fokas and Zyskin to give an integral representation to the
solution of a class of boundary value problems, in an arbitrary number of
dimensions. We present an extended example using these results in which we
construct a global relation for the linearised Navier-Stokes equations.
