We present a collection of recent results on the numerical approximation of Volterra integral
equations and integro-differential equations by means of collocation type methods, which …

The present paper illustrates some classes of multivalue methods for the numerical solution
of ordinary and fractional differential equations. In particular, it focuses on two-step and …

We introduce multistep collocation methods for the numerical integration of Volterra Integral
Equations, which depend on the numerical solution in a fixed number of previous time steps …

This paper introduces a family of barycentric rational predictor-corrector schemes based on
the Floater–Hormann family of linear barycentric rational interpolants (LBRIs) for the …

The paper is focused on the analysis of stability properties of a family of numerical methods
designed for the numerical solution of stochastic Volterra integral equations. Stability …

A new class of two-step Runge-Kutta methods for the numerical solution of ordinary
differential equations is proposed. These methods are obtained using the collocation …

Multistep collocation methods for Volterra integro-differential equations are derived and
analyzed. They increase the order of convergence of classical one-step collocation …

We develop and analyze an hp-version of the discontinuous Galerkin time-stepping method
for linear Volterra integral equations with weakly singular kernels. We derive a priori error …

The paper introduces improved stochastic ϑ-methods for the numerical integration of
stochastic Volterra integral equations. Such methods, compared to those introduced by the …

We derive exponentially fitted two-step Runge–Kutta methods for the numerical solution of
y′= f (x, y), specially tuned to the behaviour of the solution. Such methods have …