Filtering in Time-Dependent Problems

Abstract

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.