Evaluation of a Novel Filter Function With Different Exponential Powers for Alleviation of Gibbs Artifacts

The Gibbs phenomenon in series expansion representation of an irregular function has been considered as a loop hole in numerical applications. Irregularities may occur in different ways, one of which is, intrinsically contained as discontinuities in the source data, which deteriorates the approximation of function and manifests the Gibbs artifacts. Additionally, it can be occurred due to the dynamic nature or nonlinearity of model problems in terms of shocks or fronts. In this study, a novel filter function is designed, aiming at the alleviating the oscillatory phenomenon. A new approach, comprised of spectral methods and the filter function is implemented over the discontinuous function. The efficiency of proposed filter function is illustrated through illustrations with single and multiple discontinuities. Moreover, the implementation of filter function with different powers is also analyzed that revealing variations of the reconstruction and error estimate.