Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the
description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be …

Geometric integration is the numerical integration of a differential equation, while preserving
one or more of its' geometric'properties exactly, ie to within round-off error. Many of these …

This Letter proposes a new high precision energy-preserving integrator for system of
oscillatory second-order differential equations q ″(t)+ Mq (t)= f (q (t)) with a symmetric and …

A new strategy to preserve invariants in the numerical integration of initial value problems
with explicit Runge--Kutta methods is presented. It is proved that this technique retains the …

We show a novel systematic way to construct conservative finite difference schemes for
quasilinear first-order systems of ordinary differential equations with conserved quantities. In …

The discrete gradient methods are integrators designed to preserve invariants of ordinary
differential equations. From a formal series expansion of a subclass of these methods, we …

We present a class of non-standard numerical schemes which are modifications of the
discrete gradient method. They preserve the energy integral exactly (up to the round-off …

We show the arbitrarily long-term stability of conservative methods for autonomous ODEs.
Given a system of autonomous ODEs with conserved quantities, if the preimage of the …

Numerical integration of ordinary differential equations with some invariants is considered.
For such a purpose, certain projection methods have proved its high accuracy and …

Discrete gradient methods are a class of numerical integrators producing solutions with
exact preservation of first integrals of ordinary differential equations. In this paper, we apply …