Finite difference schemes with non polynomial local conservation laws

KdV equations (Korteweg-de Vries equations) (35Q53) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Vulcanology; magma and lava flow (86A70)

Cites Work

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Discrete gradient methods have an energy conservation law
A simple framework for the derivation and analysis of effective one-step methods for ODEs
A note on the efficient implementation of Hamiltonian BVMs
Energy conservation issues in the numerical solution of the semilinear wave equation
Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation
A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations
A variational complex for difference equations
Numerical methods for the solution of the third- and fifth-order dispersive Korteweg-de Vries equations
Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
Linearly implicit and second-order energy-preserving schemes for the modified Korteweg-de Vries equation
A new technique for preserving conservation laws
Linearly implicit structure-preserving schemes for Hamiltonian systems
Numerical preservation of multiple local conservation laws
Defect-based local error estimators for splitting methods, with application to Schrödinger equations. II: Higher-order methods for linear problems.
Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime
Locally conservative finite difference schemes for the modified KdV equation
Spectrally accurate space-time solution of Hamiltonian PDEs
Quadratic invariants and multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
Painlevé analysis and similarity reductions for the magma equation
Analysis of Hamiltonian boundary value methods (HBVMs): A class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
Difference Equations by Differential Equation Methods
Line Integral Methods for Conservative Problems
Discrete Variational Derivative Method
Simulating Hamiltonian Dynamics
Approximate solutions for magmon propagation from a reservoir
The Multiplier Method to Construct Conservative Finite Difference Schemes for Ordinary and Partial Differential Equations
Nonlinear waves in compacting media
Geometric integration using discrete gradients
Conservation laws for a nonlinear wave equation
Robust Defect Control with Runge–Kutta Schemes
Perturbation solution for small amplitude solitary waves in two-phase fluid flow of compacting media
Simple bespoke preservation of two conservation laws
Conservative Methods for Dynamical Systems
A new class of energy-preserving numerical integration methods
Numerical methods for Hamiltonian PDEs
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
Optimal parameters for numerical solvers of PDEs
Exponentially fitted methods with a local energy conservation law
Exponentially fitted methods that preserve conservation laws

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