Abstract:
This work is devoted to the study of wavelet schemes for solving nonlinear differential
equations. Most of the scientific and engineering phenomena can be represented in the form
of nonlinear differential equations. Over the past few decades, nonlinear differential
equations have been the core of research for many researchers and scientists. Owing to the
non-availability of exact solutions in many nonlinear physical problems representing
complex phenomena, various analytical and non-analytical schemes have been evolved.
One of the most recent families of schemes developed for finding solutions of differential
equations is Wavelet schemes. These newly revolutionized schemes have few
shortcomings, while dealing with nonlinear differential equations. The existing wavelets
schemes are being modified and enhanced in this study to overcome these shortcomings.
In this study, techniques such as Picard’s Iteration Method, Quasilinearization Method and
Method of Steps have been merged with different wavelet schemes, which proved to be
very proficient, reliable and effective in handling a large number of nonlinear mathematical
problems representing nonlinear differential equations and their systems. These wavelet
schemes have been extended for fractional nonlinear differential equations also.
