This paper introduces multivalue collocation methods for the numerical solution of stiff
problems. The presented approach does not exhibit the phenomenon of order reduction …

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

This book is focused on the numerical discretization of ordinary differential equations
(ODEs), under several perspectives. The attention is first conveyed to providing accurate …

It is the purpose of this paper to consider the employ of General Linear Methods (GLMs) as
geometric numerical solvers for the treatment of Hamiltonian problems. Indeed, even if 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 …

It is the purpose of this paper to derive diagonally implicit exponentially fitted (EF) Runge–
Kutta methods for the numerical solution of initial value problems based on first order …

We introduce a family of diagonally-implicit continuous methods for the numerical integration
of Volterra Integral Equations. The derived methods are characterized by a lower triangular …

It is the purpose of this paper to provide an acceleration of waveform relaxation (WR)
methods for the numerical solution of large systems of ordinary differential equations. The …

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 …

Abstract Two-step Runge–Kutta (TSRK) methods are Runge–Kutta methods that depend on
stage values at two consecutive steps. Second derivative Two-step Runge–Kutta (SD-TSRK) …