Spectral methods to solve nonlinear problems: A review

Abstract

The study is intended to give a brief overview of recent papers on spectral methods in different types of fluid flow especially nanofluid flow. The survey does not presume to be exhaustive; hence some selection is necessary. The papers reviewed herein relate to the recent use of some spectral based algorithms, notably the spectral relaxation method, the spectral local linearization method, the spectral quasi-linearization method, the successive linearization method, the piecewise successive linearization method and the spectral homotopy analysis method, etc. We review the important papers and problems where these methods have been used. The paper is divided into sections related to the use of each method. In addition to reviewing the journal articles in the main body of the paper, we also give details of important books published on spectral methods in fluid dynamics.