Optimal convergence of a second order low-regularity integrator for the KdV equation

10/16/2019
by   Yifei Wu, et al.
0

In this paper, we establish the optimal convergence result of a second order exponential-type integrator for solving the KdV equation under rough initial data. The scheme is explicit and efficient to implement. By rigorous error analysis, we show that the scheme provides second order accuracy in H^γ for initial data in H^γ+4 for any γ≥0, which is the lowest possible regularity requirement so far. The result is confirmed by numerical experiments and comparisons are made with the Strang splitting scheme.

READ FULL TEXT
research
08/17/2020

Embedded exponential-type low-regularity integrators for KdV equation under rough data

In this paper, we introduce a novel class of embedded exponential-type l...
research
09/02/2021

A second order low-regularity integrator for the nonlinear Schrödinger equation

In this paper, we analyse a new exponential-type integrator for the nonl...
research
03/29/2022

A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation

The numerical approximation of the semilinear Klein–Gordon equation in t...
research
01/11/2023

A semi-discrete first-order low regularity exponential integrator for the "good" Boussinesq equation without loss of regularity

In this paper, we propose a semi-discrete first-order low regularity exp...
research
07/31/2020

Numerical integrators for continuous disordered nonlinear Schrödinger equation

In this paper, we consider the numerical solution of the continuous diso...
research
06/06/2023

Second order error bounds for POD-ROM methods based on first order divided differences

This note proves, for simplicity for the heat equation, that using BDF2 ...
research
01/30/2023

A symmetric low-regularity integrator for the nonlinear Schrödinger equation

We introduce and analyze a symmetric low-regularity scheme for the nonli...

Please sign up or login with your details

Forgot password? Click here to reset