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

Sahu, Smita

Abstract

This work is based on high-order “filtered scheme”. Recently filtered scheme has been introduced to solve some first order Hamilton–Jacobi equations. In this paper, we aim to solve some linear and non-linear partial differential equations by a high order filtered scheme. The proposed filtered scheme that is not monotone but still satisfies some ϵ-monotone property with a convergence result and with precise error estimate also has been proven. We will present filtration of different schemes for some linear and non-linear partial differential equations in several dimensions.

Citation

Sahu, S. (2018). High-order filtered schemes for first order time dependent linear and non-linear partial differential equations. Mathematics and Computers in Simulation, 147, 250-263. https://doi.org/10.1016/j.matcom.2017.05.009

• Journal Article Type: Article
• Acceptance Date: May 26, 2017
• Online Publication Date: Jun 20, 2017
• Publication Date: May 1, 2018
• Deposit Date: Jun 29, 2017
• Publicly Available Date: Jun 20, 2018
• Journal: Mathematics and Computers in Simulation
• Print ISSN: 0378-4754
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 147
• Pages: 250-263
• DOI: https://doi.org/10.1016/j.matcom.2017.05.009
• Public URL: https://durham-repository.worktribe.com/output/1384047