On the Construction of Exact Numerical Schemes for Linear Delay Models

Exact numerical schemes have previously been obtained for some linear retarded delay differential equations and systems. Those were derived from explicit expressions of the exact solutions, expressed in form perturbed difference systems, involving values at previous intervals. In this work, we propose to directly obtain same type fundamental solutions equations, by considering vector with components corresponding delay-lagged From these arbitrary initial functions can be proposed, they may also facilitate obtaining solutions. We apply approach an scheme first order neutral equation x′(t)−γx′(t−τ)=αx(t)+βx(t−τ), general condition x(t)=φ(t) −τ≤t≤0. The resulting expression reduces those published when γ=0.