A new third-order EXP-WENO scheme for Hamilton–Jacobi equations

Rooholah Abedian ()
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Rooholah Abedian: School of Engineering Science, College of Engineering, University of Tehran, Iran

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 06, 1-21

Abstract: The authors of this research paper have introduced a new method for solving Hamilton–Jacobi (HJ) equations called third-order weighted essentially nonoscillatory (WENO) method. This method uses exponential polynomials to construct numerical fluxes and smoothness indicators, which helps distinguish between singular and smooth regions more efficiently. The smoothness indicators are created using a finite difference operator that eliminates exponential polynomials. The numerical flux is constructed using an interpolation method based on exponential polynomials, which results in better outcomes around steep gradients. The new method maintains a high level of accuracy (i.e. three) in smooth regions, even near critical points. The authors have presented some numerical results to demonstrate the effectiveness of the new method and compared it with other WENO methods.

Keywords: Weighted essentially; nonoscillatory scheme; finite difference framework; Hamilton–Jacobi equations; smoothness indicator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500785

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