Open AccessA Study of Legendre Polynomials Approximation for Solving Initial Value Problems
Author(s) -
Oday I. Al-Shaher,
Mohammed S. Mechee
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1897/1/012058
Subject(s) - legendre polynomials , legendre wavelet , mathematics , associated legendre polynomials , legendre function , classical orthogonal polynomials , orthogonal polynomials , legendre's equation , ordinary differential equation , basis function , gaussian , initial value problem , numerical analysis , gegenbauer polynomials , differential equation , mathematical analysis , computer science , physics , discrete wavelet transform , wavelet transform , artificial intelligence , wavelet , quantum mechanics
Legendre polynomials (LPs) basis on the interval I = [-1;1] have been introduced and their properties are studied. Legendre polynomials with Gaussian integration method (GIM) are used to solve the initial value problems (IVPs) of third-order ordinary differential equations (ODEs). The aim of this work is to study the numerical solution of IVP which is widely applicable in the fields of engineering and science using Legendre base. The implementations have been discussed to demonstrate the validity and applicability of the technique of collections and variational methods which compared with the numerical results that obtained by classical RK and modern direct RKD numerical methods. Finally, the numerical results show the high accuracy and efficiency of the proposed method.