Solving the Korteweg-de Vries equation with Hermite-based finite differences

作者：

Highlights：

• The new Hermite-based finite differences has several advantages over finite differences.

• Reduced dispersion and trailing waves errors while stencils are more compact.

• Points per wavelength are improved in the context of the 1D transport equation.

• Improvements when solving the KdV equation over standard finite differences.

摘要

•The new Hermite-based finite differences has several advantages over finite differences.•Reduced dispersion and trailing waves errors while stencils are more compact.•Points per wavelength are improved in the context of the 1D transport equation.•Improvements when solving the KdV equation over standard finite differences.

论文关键词：Hermite,Finite difference,Partial differential equations,KdV,Non-linear PDE

论文评审过程：Received 1 July 2020, Revised 28 December 2020, Accepted 11 February 2021, Available online 25 February 2021, Version of Record 25 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126101