Performance Analysis of Different Filters For Gibbs Phenomenon Minimization: A Comparative Study

When the approximated function is smooth enough, spectral methods have superior resolution; however, the approximation is plagued by dynamic Gibbs oscillations if the function has discontinuities within the given domain. Using the filtering process, it is possible to recover spectral accuracy for nonsmooth functions. This paper proposes a filter function for filtering the expansion coefficients. To perform the approximation, filtered Chebyshev spectral method has been considered in conjunction with proposed filter function. To elaborate the efficiency of proposed filter, illustrations have been taken for piecewise continuous functions. The comparison analysis with pre-existing filters function is also made. The error analysis is provided through mean squared difference error and maximum error.