High-order filtered schemes for first order time dependent linear and non-linear partial differential equations

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Abstract

This work is based on high-order “filtered scheme”. Recently filtered scheme has been introduced to solve some first orderHamilton–Jacobi equations. In this paper, we aim to solve some linear and non-linear partial differential equations by a highorder filtered scheme. The proposed filtered scheme that is not monotone but still satisfies someε-monotone property with aconvergence result and with precise error estimate also has been proven. We will present filtration of different schemes for somelinear and non-linear partial differential equations in several dimensions.
Original languageEnglish
Pages (from-to)250-263
Number of pages14
JournalMathematics and Computers in Simulation
Volume147
Early online date20 Jun 2017
DOIs
Publication statusPublished - May 2018

Keywords

  • Hamilton–Jacobi equation
  • High-order schemes
  • Semi-Lagrangian schemes
  • Viscosity solutions
  • ϵ-monotone scheme

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