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05/26/2023
Symmetric resonance based integrators and forest formulae
We introduce a unified framework of symmetric resonance based schemes wh...
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02/01/2023
Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
We introduce a new non-resonant low-regularity integrator for the cubic ...
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01/25/2023
Low regularity error estimates for the time integration of 2D NLS
A filtered Lie splitting scheme is proposed for the time integration of ...
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11/17/2022
Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine–Gordon equation
We establish the improved uniform error bounds on a Lawson-type exponent...
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11/08/2022
Low regularity integrators for semilinear parabolic equations with maximum bound principles
This paper is concerned with conditionally structure-preserving, low reg...
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11/02/2022
Numerical integration of Schrödinger maps via the Hasimoto transform
We introduce a numerical approach to computing the Schrödinger map (SM) ...
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05/10/2022
Bridging the gap: symplecticity and low regularity on the example of the KdV equation
Recent years have seen an increasing amount of research devoted to the d...
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05/04/2022
Approximations of dispersive PDEs in the presence of low-regularity randomness
We introduce a new class of numerical schemes which allow for low regula...
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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...
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02/02/2022
Low regularity integrators via decorated trees
We introduce a general framework of low regularity integrators which all...
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12/16/2021
Effective high order integrators for linear Klein-Gordon equations in low to highly oscillatory regimes
We introduce an efficient class of high order schemes for the Klein–Gord...
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07/28/2021
A semi-implicit low-regularity integrator for Navier-Stokes equations
A new type of low-regularity integrator is proposed for Navier-Stokes eq...
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05/08/2021
Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter
We propose a new class of uniformly accurate splitting methods for the B...
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05/08/2021
Time integrators for dispersive equations in the long wave regime
We introduce a novel class of time integrators for dispersive equations ...
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04/23/2021
Uniformly accurate low regularity integrators for the Klein–Gordon equation from the classical to non-relativistic limit regime
We propose a novel class of uniformly accurate integrators for the Klein...
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02/22/2021
Convergence error estimates at low regularity for time discretizations of KdV
We consider various filtered time discretizations of the periodic Kortew...
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01/31/2021
Solving the linear semiclassical Schrödinger equation on the real line
The numerical solution of a linear Schrödinger equation in the semiclass...
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12/28/2020
Error estimates at low regularity of splitting schemes for NLS
We study a filtered Lie splitting scheme for the cubic nonlinear Schrödi...
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12/27/2020
Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation
We carry out the convergence analysis of the Scalar Auxiliary Variable (...
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10/04/2020
A general framework of low regularity integrators
We introduce a new general framework for the approximation of evolution ...
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06/23/2020
Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces
In this paper, we propose a new scheme for the integration of the period...
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05/04/2020
Resonance based schemes for dispersive equations via decorated trees
We introduce a numerical framework for dispersive equations embedding th...
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06/22/2019