Abstract :
In this paper, we give a survey of the existing literature on singularly perturbed Volterra integral and integro-differential equations. A link to closely related problems, namely integro-differential-algebraic and integralalgebraic equations, is established. This paper also contains two original contributions. We show how asymptotic expansions of solutions can be easily derived in the linear convolution case. We give convergence results for linear multistep methods applied to singularly perturbed, possibly weakly singular Volterra integral equations and we present numerical illustrations.
