Some Wavelet Schemes for Nonlinear Differential Equations

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.