Open AccessShifted-Legendre orthonormal method for high-dimensional heat conduction equations
Author(s) -
Liangcai Mei,
Boying Wu,
Lin Yang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022525
Subject(s) - legendre polynomials , convergence (economics) , orthonormal basis , mathematics , thermal conduction , space (punctuation) , mathematical analysis , legendre wavelet , order (exchange) , computer science , physics , quantum mechanics , economics , thermodynamics , economic growth , operating system , finance , discrete wavelet transform , wavelet transform , artificial intelligence , wavelet
In this paper, a numerical alogorthm for solving high-dimensional heat conduction equations is proposed. Based on Shifted-Legendre orthonormal polynomial and $ \varepsilon- $best approximate solution, we extend the algorithm from low-dimensional space to high-dimensional space, and prove the convergence of the algorithm. Compared with other numerical methods, the proposed algorithm has the advantages of easy expansion and high convergence order, and we prove that the algorithm has $ \alpha $-Order convergence. The validity and accuracy of this method are verified by some numerical experiments.