publications

2026

1. SIAM J. Numer. Anal.

   Computing rough solutions of the KdV equation below L^2

   Jiachuan Cao , Buyang Li, Yifei Wu, and Fangyan Yao

   SIAM Journal on Numerical Analysis, 2026

   arXiv Bib

   @article{Cao-Li-Wu-Yao-2026,
     author = {Cao, Jiachuan and Li, Buyang and Wu, Yifei and Yao, Fangyan},
     title = {Computing rough solutions of the KdV equation below $L^2$},
     journal = {SIAM Journal on Numerical Analysis},
     year = {2026},
     url = {https://arxiv.org/abs/2506.21969},
   }

2. Numer. Math.

   Second-order uniformly accurate method for the semiclassical nonlinear Schrödinger equation with initial data in H^2

   Buyang Li, Yifei Wu, and Fangyan Yao

   Numerische Mathematik, 2026

   DOI Bib

   @article{Li-Wu-Yao-2026,
     author = {Li, Buyang and Wu, Yifei and Yao, Fangyan},
     title = {Second-order uniformly accurate method for the semiclassical nonlinear Schrödinger equation with initial data in 
     $H^2$},
     journal = {Numerische Mathematik},
     year = {2026},
     doi = {10.1007/s00211-026-01541-7},
     url = {https://link.springer.com/article/10.1007/s00211-026-01541-7},
   }

2025

1. SIAM J. Numer. Anal.

   Numerical approximation of discontinuous solutions of the semilinear wave equation

   Jiachuan Cao , Buyang Li, Yanping Lin, and Fangyan Yao

   SIAM Journal on Numerical Analysis, 2025

   DOI arXiv Bib

   @article{Cao-Li-Lin,
     author = {Cao, Jiachuan and Li, Buyang and Lin, Yanping and Yao, Fangyan},
     title = {Numerical approximation of discontinuous solutions of the semilinear wave equation},
     journal = {SIAM Journal on Numerical Analysis},
     year = {2025},
     doi = {10.1137/24M1635879},
   }

2024

1. Convergence of a moving window method for the Schrödinger equation with potential on R^d

   Arieh Iserles , Buyang Li, and Fangyan Yao

   2024

   Preprint

   Bib

   @unpublished{Iserles-Li-Yao,
     author = {Iserles, Arieh and Li, Buyang and Yao, Fangyan},
     title = {Convergence of a moving window method for the Schr\"odinger equation with potential on R^d},
     note = {Preprint},
     url = {https://arxiv.org/abs/2408.09463},
     year = {2024},
   }

2023

1. A fully discrete low-regularity integrator for the Korteweg-de Vries equation

   Yongsheng Li, and Fangyan Yao

   Communications in Mathematical Sciences, 2023

   DOI Bib

   @article{Li-Yao-2023,
     author = {Li, Yongsheng and Yao, Fangyan},
     title = {A fully discrete low-regularity integrator for the Korteweg-de Vries equation},
     journal = {Communications in Mathematical Sciences},
     year = {2023},
     volume = {21},
     number = {7},
     pages = {1917--1935},
     dimensions = {true},
     doi = {10.4310/CMS.2023.v21.n7.a8},
     url = {https://dx.doi.org/10.4310/CMS.2023.v21.n7.a8}
   }

2022

1. Math. Comp.

   A first-order Fourier integrator for the nonlinear Schrödinger equation on T without loss of regularity

   Yifei Wu, and Fangyan Yao

   Mathematics of Computation, 2022

   DOI Bib

   @article{Wu-Yao,
     author = {Wu, Yifei and Yao, Fangyan},
     title = {A first-order Fourier integrator for the nonlinear Schrödinger equation on T without loss of regularity},
     journal = {Mathematics of Computation},
     year = {2022},
     volume = {91},
     doi = {10.1090/mcom/3705},
     number = {335},
     dimensions = {true},
     pages = {1212--1235},
     url = {https://www.ams.org/journals/mcom/2022-91-335/S0025-5718-2021-03705-9/home.html},
   }

2. A fully discrete low-regularity integrator for the nonlinear Schrödinger equation

   Alexander Ostermann, and Fangyan Yao

   Journal of Scientific Computing, 2022

   DOI Bib

   @article{Ostermann-Yao,
     author = {Ostermann, Alexander and Yao, Fangyan},
     title = {A fully discrete low-regularity integrator for the nonlinear Schr\"odinger equation},
     journal = {Journal of Scientific Computing},
     year = {2022},
     volume = {91},
     number = {1},
     pages = {9},
     dimensions = {true},
     doi = {10.1007/s10915-022-01786-y},
     url = {https://link.springer.com/10.1007/s10915-022-01786-y},
   }

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

   Alexander Ostermann, Yifei Wu, and Fangyan Yao

   Advances in Continuous and Discrete Models: Theory and Applications, 2022

   Bib

   @article{Ostermann-Wu-Yao,
     author = {Ostermann, Alexander and Wu, Yifei and Yao, Fangyan},
     title = {A second-order low-regularity integrator for the nonlinear Schrödinger equation},
     journal = {Advances in Continuous and Discrete Models: Theory and Applications},
     year = {2022},
     volume = {23},
     url = {https://ncesindifferenceequations.springeropen.com/articles/10.1186/s13662-022-03695-8}
   }

4. A second-order embedded low-regularity integrator for the quadratic nonlinear Schrödinger equation

   Fangyan Yao

   International Journal of Numerical Analysis and Modeling, 2022

   Bib

   @article{Yao,
     author = {Yao, Fangyan},
     title = {A second-order embedded low-regularity integrator for the quadratic nonlinear Schr\"odinger equation},
     journal = {International Journal of Numerical Analysis and Modeling},
     year = {2022},
     volume = {19},
     number = {5},
     pages = {656--668},
     url = {https://global-sci.org/intro/article_detail/ijnam/20931.html}
   }

2021

1. Convergence of an embedded exponential-type low-regularity integrator for the KdV equation without loss of regularity

   Yongsheng Li, Yifei Wu, and Fangyan Yao

   Annals of Applied Mathematics, 2021

   DOI Bib

   @article{Li-Wu-Yao,
     author = {Li, Yongsheng and Wu, Yifei and Yao, Fangyan},
     title = {Convergence of an embedded exponential-type low-regularity integrator for the KdV equation without loss of regularity},
     journal = {Annals of Applied Mathematics},
     year = {2021},
     volume = {37},
     doi = {10.4208/aam.OA-2020-0001},
     dimensions = {true},
     number = {1},
     pages = {1--21},
     url = {http://global-sci.org/intro/article_detail/aam/18628.html}
   }

2. Derivation of the nonlinear Schrödinger equation with a general nonlinearity and Gross-Pitaevskii hierarchy in one and two dimensions

   Yongsheng Li, and Fangyan Yao

   Journal of Mathematical Physics, 2021

   Bib

   @article{Li-Yao-2021,
     author = {Li, Yongsheng and Yao, Fangyan},
     title = {Derivation of the nonlinear Schr\"odinger equation with a general nonlinearity and Gross-Pitaevskii hierarchy in one and two dimensions},
     journal = {Journal of Mathematical Physics},
     year = {2021},
     volume = {62},
     number = {2},
     pages = {021505},
     url = {https://pubs.aip.org/aip/jmp/article-abstract/62/2/021505/234535/Derivation-of-the-nonlinear-Schrodinger-equation}
   }