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 …

Probabilistic solvers for ordinary differential equations assign a posterior measure to the
solution of an initial value problem. The joint covariance of this distribution provides an …

For many systems of differential equations modeling problems in science and engineering,
there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff …

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

We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta
methods for ordinary differential equations with both non-stiff and stiff components. The …

The present paper illustrates the construction of direct quadrature methods of arbitrary order
for Volterra integral equations with periodic solution. The coefficients of these methods …

We propose two-step collocation methods for the numerical solution of fractional differential
equations. These methods increase the order of convergence of one-step collocation …

This paper deals with the numerical solution of systems of differential equations with a stiff
part and a non-stiff one, typically arising from the semi-discretization of certain partial …

It is the purpose of this paper to construct an error estimation for highly stable two-step
continuous methods derived in [7], in order to use it in a variable stepsize implementation …

Internet has become very popular all over the world, due to the low cost services and the
huge number of opportunities it offers. Nowadays, social media represents the main tool of …