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Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation $y^{\text{'}}\left(t\right)=\gamma y\left(t\right)+{\int }_0^t(\lambda +\mu t+vs)y\left(s\right)ds$ and absolute stability is deffined in terms of the real parameters $\gamma ,\lambda ,\mu$ and $v$. Sufficient conditions are illustrated for $(0;0)$ - methods and for combinations of Adams-Moulton and backward differentiation methods.

A numerical method for the solution of a second order boundary value problem for differential equation with state dependent deviating argument is studied. Second-order convergence is established and a theorem about the asymptotic expansion of global discretization error is given. This theorem makes it possible to improve the accuracy of the numerical solution by using Richardson extrapolation which results in a convergent method of order three. This is in contrast to boundary value problems for...