# Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces

@article{Bhatt2019ExponentialIP, title={Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces}, author={Ashish Bhatt and Brian E. Moore}, journal={J. Comput. Appl. Math.}, year={2019}, volume={352}, pages={341-351} }

## 9 Citations

Multi-Symplectic Method for the Logarithmic-KdV Equation

- Mathematics, PhysicsSymmetry
- 2020

Using the multi-symplectic integrator, the numerical simulation of the Gaussian solitary wave propagation of the logarithmic Korteweg–de Vries (logarithic-KdV) equation was investigated.

Complete Classification of Local Conservation Laws for Generalized Kuramoto-Sivashinsky Equation

- Mathematics
- 2021

For an arbitrary number of spatial independent variables we present a complete list of cases when the generalized Kuramoto–Sivashinsky equation admits nontrivial local conservation laws of any order,…

A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions

- MathematicsAdv. Comput. Math.
- 2020

An optimal L 2 -error estimate for the proposed Fourier pseudo-spectral method without any restriction on the grid ratio is established by analyzing the real and imaginary parts of the error function.

Comparaison of Exponential integrators and traditional time integration schemes for the Shallow Water equations

- Environmental Science, Mathematics
- 2020

The time integration scheme is probably one of the most fundamental choice in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the…

A linearized and conservative Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation in three dimensions

- Mathematics
- 2018

An optimal $L^2$-error estimate for the proposed Fourier pseudo-spectral method without any restriction on the grid ratio is established by analyzing the real and imaginary parts of the error function.

Nonexistence of local conservation laws for generalized Swift–Hohenberg equation

- MathematicsJournal of Mathematical Chemistry
- 2021

We prove that the generalized Swift–Hohenberg equation with nonlinear right-hand side, a natural generalization of the Swift–Hohenberg equation arising in physics, chemistry and biology and…

Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

- Applied Numerical Mathematics
- 2022

Exponential Integrators Based on Discrete Gradients for Linearly Damped/Driven Poisson Systems

- MathematicsJ. Sci. Comput.
- 2021

On dissipative symplectic integration with applications to gradient-based optimization

- Computer Science, Mathematics
- 2020

A generalization of symplectic integrators to non-conservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error, enabling the derivation of ‘rate-matching’ algorithms without the need for a discrete convergence analysis.

## References

SHOWING 1-10 OF 52 REFERENCES

Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems

- MathematicsJ. Sci. Comput.
- 2016

Numerical methods for solving linearly damped Hamiltonian systems are constructed using the popular Störmer–Verlet and implicit midpoint methods, and additional structure preservation is discovered for the discretized PDEs.

Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method

- Mathematics, PhysicsJ. Comput. Phys.
- 2012

Structure-preserving Exponential Runge-Kutta Methods

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2017

Numerical experiments illustrate the higher-order accuracy and structure-preserving properties of various ERK methods, demonstrating clear advantages over classical conservative Runge--Kutta methods.

Conformal conservation laws and geometric integration for damped Hamiltonian PDEs

- Physics, MathematicsJ. Comput. Phys.
- 2013

Conformal structure-preserving method for damped nonlinear Schrödinger equation*

- Physics
- 2016

In this paper, we propose a conformal momentum-preserving method to solve a damped nonlinear Schrodinger (DNLS) equation. Based on its damped multi-symplectic formulation, the DNLS system can be…

Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

A novel stable and efficient dissipation-preserving method for acoustic wave propagations in attenuating media with both correct phase and amplitude and the intrinsic dissipation law and the conformal symplectic conservation law are revealed.

Backward error analysis for multi-symplectic integration methods

- PhysicsNumerische Mathematik
- 2003

The ideas of symplectic integration are extended to Hamiltonian PDEs, and this paves the way for the development of a local modified equation analysis solely as a useful diagnostic tool for the study of these types of discretizations.

A modified equations approach for multi-symplectic integration methods.

- Physics
- 2003

A useful method for understanding discretization error in the numerical solution of ODEs is to compare the system of ODEs with the modified equations, the equations solved by the numerical solution,…

Almost structure-preserving analysis for weakly linear damping nonlinear Schrödinger equation with periodic perturbation

- Physics, MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2017