3 papers
math.NA2025
Computing rough solutions of the KdV equation below
Jiachuan Cao, Buyang Li, Yifei Wu +1
We establish a novel numerical and analytical framework for solving the Korteweg--de Vries (KdV) equation in the negative Sobolev spaces, where classical numerical methods fail due…
math.NA2024
Numerical approximation of discontinuous solutions of the semilinear wave equation
Jiachuan Cao, Buyang Li, Yanping Lin +1
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The pr…
math.NA2024
Convergence of a moving window method for the Schrödinger equation with potential on
Arieh Iserles, Buyang Li, Fangyan Yao
We propose a novel framework, called moving window method, for solving the linear Schrödinger equation with an external potential in . This method employs a smooth c…