Open AccessA New Boubaker Wavelets Operational Matrix of Integration
Author(s) -
Mohammed Abdelhadi Sarhan,
Suha Shihab,
Mohammed Rasheed
Publication year - 2020
Publication title -
xi'nan jiaotong daxue xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 21
ISSN - 0258-2724
DOI - 10.35741/issn.0258-2724.55.2.3
Subject(s) - wavelet , legendre wavelet , mathematics , matrix (chemical analysis) , algebraic equation , mathematical optimization , algebraic number , singular value , computer science , mathematical analysis , wavelet transform , algebra over a field , algorithm , discrete wavelet transform , pure mathematics , artificial intelligence , eigenvalues and eigenvectors , physics , materials science , nonlinear system , quantum mechanics , composite material
Many fields of science and engineering have used wavelet functions. They are established from expansion of a single mother wavelet function. Boubaker wavelet functions are presented in this paper based on the important properties of Boubaker polynomials. The research goal of this article is to drive a Boubaker wavelets operation matrix of integration in general formulas. Then an approximate solution method for solving a singular initial value problem is presented using Boubaker wavelets along the obtained operational matrix of integration. The importance of this method is that it converts a singular initial value problem in order to solve algebraic examples as a system. The process is based on reducing by means of integration the original problem into integral equations using a Boubaker wavelets operation matrix of integration to predict the integral equation. Illustrative experiments are included. In addition, computational results obtained by a Boubaker wavelets operation matrix of integration are compared with the exact solutions and other existing methods.