ABSTRACT
This chapter discusses the basic ideas of some well-known analytical techniques such as variational iteration method (VIM), first integral method (FIM), homotopy perturbation method (HPM), homotopy analysis method (HAM), optimal homotopy asymptotic method (OHAM). It examines the applicability of the proposed methods for solving nonlinear partial differential equations (PDEs) and fractional partial differential equations (FPDEs). The subject of wavelet analysis has recently drawn a great deal of attention from mathematical scientists in various disciplines. Some view wavelets as a new basis for representing functions, some consider it as a technique for time-frequency analysis, and others think of it as a new mathematical subject. Wavelets are very effectively used in signal analysis for wave form demonstration and segmentations, time-frequency analysis, medical diagnostics, geophysical signal processing, statistical analysis, pattern recognition, and fast algorithms for easy execution. The chapter introduces different wavelet-based methods, namely, the Haar wavelet method, the Legendre wavelet method (LWM), the Chebyshev wavelet method (CWM), the Hermite wavelet method (HWM).
