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Mollification of Fourier Spectral Methods with Polynomial Kernels
  • Chandhini G,
  • Megha P
Chandhini G
National Institute of Technology Karnataka

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Megha P
National Institute of Technology Karnataka
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Many attempts have been made in the past to regain the spectral accuracy of the spectral methods, which is lost drastically due to the presence of discontinuity. In this article, an attempt has been made to show that mollification using Legendre and Chebyshev polynomial based kernels improves the convergence rate of the Fourier spectral method. Numerical illustrations are provided with examples involving one or more discontinuities and compared with the existing Dirichlet kernel mollifier. Dependence of the efficiency of the polynomial mollifiers on the parameter P is analogous to that in the Dirichlet mollifier, which is detailed by analysing the numerical solution. Further, they are extended to linear scalar conservation law problems.
03 Apr 2023Submitted to Mathematical Methods in the Applied Sciences
03 Apr 2023Submission Checks Completed
03 Apr 2023Assigned to Editor
08 Apr 2023Review(s) Completed, Editorial Evaluation Pending
09 Apr 2023Reviewer(s) Assigned
30 Jul 2023Editorial Decision: Revise Major
15 Oct 20231st Revision Received
20 Oct 2023Submission Checks Completed
20 Oct 2023Assigned to Editor
20 Oct 2023Review(s) Completed, Editorial Evaluation Pending
21 Oct 2023Reviewer(s) Assigned