El-Shazly, N.; Ramadan, M.; Radwan, T. Generalized Legendre Wavelets, Definition, Properties and Their Applications for Solving Linear Differential Equations. Egyptian Journal of Pure and Applied Science 2023, 62, 20–32, doi:10.21608/ejaps.2023.252206.1080.
El-Shazly, N.; Ramadan, M.; Radwan, T. Generalized Legendre Wavelets, Definition, Properties and Their Applications for Solving Linear Differential Equations. Egyptian Journal of Pure and Applied Science 2023, 62, 20–32, doi:10.21608/ejaps.2023.252206.1080.
El-Shazly, N.; Ramadan, M.; Radwan, T. Generalized Legendre Wavelets, Definition, Properties and Their Applications for Solving Linear Differential Equations. Egyptian Journal of Pure and Applied Science 2023, 62, 20–32, doi:10.21608/ejaps.2023.252206.1080.
El-Shazly, N.; Ramadan, M.; Radwan, T. Generalized Legendre Wavelets, Definition, Properties and Their Applications for Solving Linear Differential Equations. Egyptian Journal of Pure and Applied Science 2023, 62, 20–32, doi:10.21608/ejaps.2023.252206.1080.
Abstract
In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.
Keywords
Generalized Legendre wavelet; operational matrix of integration; linear differential equations; product operation matrix; convergence analysis; accuracy
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
