This work focuses on the linear two-point boundary value
problem
y’ = A(x)y + f(x), a < x < b
Bay(a) + Bby(b) = y
with a view to their solution by some form of parallel
algorithm. The theory and practice of current sequential
solution methods is reviewed to select a method which
exhibits concurrent processing potential. The method selected is a version of multiple shooting. The language Ada is chosen to code the algorithm because of the features available in it, particularly the inbuilt tasking facility for concurrent processing. The efficiency of the parallel code as implemented is demonstrated by a series of numerical experiments, the results of which are summarised m tabular form.