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.
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