Browsing by Author "Megha, P."

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    Filtering in Time-Dependent Problems
    (Springer, 2023) Megha, P.; Godavarma, G.
    Spectral methods are efficient, robust and highly accurate methods in numerical analysis. When it comes to approximating a discontinuous function with spectral methods, it produces spurious oscillations at the point of discontinuity, which is called Gibbs’ phenomenon. Gibbs’ phenomenon reduces the spectral accuracy of the method globally. Filtering is a widely used method to prevent the oscillations due to Gibbs’ phenomenon by which the accuracy of the spectral methods is regained up to an extent. In this work, we study the effects of various filters in time-dependent problems and do a comparison of numerical results. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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    Spectral error bound in the mollification of Fourier approximation using Gegenbauer polynomial based mollifier
    (Springer Nature, 2025) Megha, P.; Godavarma, G.
    Due to the global nature of the Fourier spectral methods, the Fourier approximation of discontinuous function gets impaired by spurious oscillations. This results in the approximation order reducing to and, respectively, for the discontinuous and non-discontinuous points. Nevertheless, it is shown by Gottlieb and others that higher order information is hidden in this approximation, using which spectral order accuracy can be recovered. Thus, in our work, we propose a spectral mollifier using the Gegenbauer polynomial kernel to regain the spectral accuracy of the Fourier approximation of a discontinuous function. Pointwise spectral accuracy has also been proved except for the discontinuous points. Results have been illustrated through examples. © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.