[图书][B] Discrete variational derivative method: a structure-preserving numerical method for partial differential equations
D Furihata, T Matsuo - 2010 - books.google.com
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the
description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be …
description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be …
Geometric integrators for ODEs
RI McLachlan, GRW Quispel - Journal of Physics A: Mathematical …, 2006 - iopscience.iop.org
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 …
one or more of its' geometric'properties exactly, ie to within round-off error. Many of these …
A new high precision energy-preserving integrator for system of oscillatory second-order differential equations
B Wang, X Wu - Physics Letters A, 2012 - Elsevier
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 …
oscillatory second-order differential equations q ″(t)+ Mq (t)= f (q (t)) with a symmetric and …
On the preservation of invariants by explicit Runge--Kutta methods
M Calvo, D Hernández-Abreu, JI Montijano… - SIAM Journal on …, 2006 - SIAM
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 …
with explicit Runge--Kutta methods is presented. It is proved that this technique retains the …
Conservative methods for dynamical systems
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 …
quasilinear first-order systems of ordinary differential equations with conserved quantities. In …
Order theory for discrete gradient methods
S Eidnes - BIT Numerical Mathematics, 2022 - Springer
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 …
differential equations. From a formal series expansion of a subclass of these methods, we …
Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
JL Cieśliński, B Ratkiewicz - Journal of Physics A: Mathematical …, 2011 - iopscience.iop.org
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 …
discrete gradient method. They preserve the energy integral exactly (up to the round-off …
On the arbitrarily long-term stability of conservative methods
ATS Wan, JC Nave - SIAM Journal on Numerical Analysis, 2018 - SIAM
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 …
Given a system of autonomous ODEs with conserved quantities, if the preimage of the …
Invariants preserving schemes based on explicit Runge–Kutta methods
H Kojima - BIT Numerical Mathematics, 2016 - Springer
Numerical integration of ordinary differential equations with some invariants is considered.
For such a purpose, certain projection methods have proved its high accuracy and …
For such a purpose, certain projection methods have proved its high accuracy and …
[PDF][PDF] Derivative-free discrete gradient methods
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 …
exact preservation of first integrals of ordinary differential equations. In this paper, we apply …