On the Stability of Multistep Formulas for Systems of Volterra Integro-Differential Equations

摘要

The stability behavior of linear multistep methods is analyzed for systems of integro-differential equations of Volterra type which are only restricted by the condition that the kernel function is finitely decomposable. Stability regions are derived for backward differentiation type schemes of orders 2 up to 6 and for the trapezoidal rule. In particular, attention is paid to these schemes when applied to the special integro-differential equation, which arises from differentiating a Volterra integral equation of the second kind. Numerical experiments are reported which confirm the theoretical stability results.