Open AccessAn Efficient Algorithm for Solving Variational Problems Using Hermite Polynomials
Author(s) -
Halah Rahman Jaber
Publication year - 2021
Publication title -
magallaẗ kulliyyaẗ al-rāfidayn al-ǧāmi'aẗ al-'ulūm/maǧallaẗ kulliyyaẗ al-rāfidayn al-ǧāmiʻaẗ li-l-ʻulūm
Language(s) - English
Resource type - Journals
eISSN - 2790-2293
pISSN - 1681-6870
DOI - 10.55562/jrucs.v35i1.275
Subject(s) - hermite polynomials , mathematics , classical orthogonal polynomials , algebraic number , orthogonal polynomials , hermite spline , discrete orthogonal polynomials , boundary value problem , matrix (chemical analysis) , algorithm , difference polynomials , gegenbauer polynomials , algebraic equation , algebra over a field , mathematical analysis , pure mathematics , statistics , materials science , physics , nonlinear system , quantum mechanics , bilinear interpolation , smoothing spline , composite material , spline interpolation
An algorithm for solving variational problems with fixed and free boundary conditions using Hermite polynomials is proposed. The properties of Hermite polynomials with the operational matrix of integration are used to reduce a variational problem to the solution of algebraic equations. The method verifies an accurate approximate solution with using small numbers of polynomials comparing to other methods. Several examples have been applied to the proposed method.