This paper is concerned with the study of numerical methods for ordinary
and partial
differential equations with both fixed and distributed delays. We focus
first on a delay-dependent stability
analysis of scalar ordinary differential equations with real coefficients.
The exact stability region of the trapezium
rule is desired.
It is proved that the time discretization based on the trapezium rule can
preserve the
asmptotic stability of the underlying test problems. Next, we consider
partial delay differential equations.
We show that the space discretization leads to a reduction of stability
region if the standard second-order central difference operator is employed
to approximate the Laplacian.
Finally, some numerical examples are given to confirm the theoretical
results.