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

by   Yifei Wu, et al.

In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal convergence results under rough initial data. The schemes are explicit and efficient to implement. By rigorous error analysis, we first show that the ELRI scheme provides the first order accuracy in H^γ for initial data in H^γ+1 for γ>1/2. Moreover, by adding two more correction terms to the first order scheme, we show a second order ELRI that provides the second order accuracy in H^γ for initial data in H^γ+3 for γ≥0. The proposed ELRIs further reduce the regularity requirement of existing methods so far for optimal convergence. The theoretical results are confirmed by numerical experiments, and comparisons with existing methods illustrate the efficiency of the new methods.



There are no comments yet.


page 1

page 2

page 3

page 4


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

In this paper, we establish the optimal convergence result of a second o...

Low-regularity integrators for nonlinear Dirac equations

In this work, we consider the numerical integration of the nonlinear Dir...

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

In this paper, we analyse a new exponential-type integrator for the nonl...

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...

Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity

We analyse a class of time discretizations for solving the Gross-Pitaevs...

Numerical integrators for continuous disordered nonlinear Schrödinger equation

In this paper, we consider the numerical solution of the continuous diso...

Semi-explicit integration of second order for weakly coupled poroelasticity

We introduce a semi-explicit time-stepping scheme of second order for li...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.