by boundary value methods (BVMs), where y(t),
f(t), f(t): R ® Rn; Jn,
Dn(1), ¼, Dn(s) Î Rn×n and
t1, ¼, ts > 0 are some constants. Such kind of
equation appears in many applications. Our methods proposed here
require the solution of some nonsymmetric, large and sparse linear
systems. The GMRES method with the Strang-type block-circulant
preconditioner is proposed for solving these linear systems. We
show that if an Ak1,k2-stable BVM is used for solving an
n-by-n system of differential equations with multi-delays,
then our preconditioner is invertible and all the eigenvalues of
the preconditioned system are clustered. It follows that when the
GMRES method is applied to solving the preconditioned systems, the
method would converge fast. Numerical results are given to show
the effectiveness of our methods.