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Computational Methods in Applied Mathematics

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Volume 18, Issue 4


High-Order Semi-Discrete Central-Upwind Schemes with Lax–Wendroff-Type Time Discretizations for Hamilton–Jacobi Equations

Rooholah AbedianORCID iD: http://orcid.org/0000-0002-1739-5964
Published Online: 2017-08-26 | DOI: https://doi.org/10.1515/cmam-2017-0031


A new fifth-order, semi-discrete central-upwind scheme with a Lax–Wendroff time discretization procedure for solving Hamilton–Jacobi (HJ) equations is presented. This is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge–Kutta time discretizations. Unlike most of the commonly used high-order upwind schemes, the new scheme is formulated as a Godunov-type method. The new scheme is based on the flux Kurganov, Noelle and Petrova (KNP flux). The spatial discretization is based on a symmetrical weighted essentially non-oscillatory reconstruction of the derivative. Following the methodology of the classic WENO procedure, non-oscillatory weights are then calculated from the ideal weights. Various numerical experiments are performed to demonstrate the accuracy and stability properties of the new method. As a result, comparing with other fifth-order schemes for HJ equations, the major advantage of the new scheme is more cost effective for certain problems while the new method exhibits smaller errors without any increase in the complexity of the computations.

Keywords: Hamilton–Jacobi Equations; Central-Upwind Schemes; Semi-Discrete Methods; Lax–Wendroff-Type Time Discretization; Central Schemes

MSC 2010: 35L99; 65M06


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About the article

Received: 2017-02-02

Revised: 2017-06-29

Accepted: 2017-08-08

Published Online: 2017-08-26

Published in Print: 2018-10-01

Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 4, Pages 559–580, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0031.

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