Open AccessSome practical remarks in solving partial differential equations using reduced order schemes obtained through the POD method
Author(s) -
Alexandru SOLOMON,
Valentin Claudiu OLTEI,
Alina Bogoi
Publication year - 2022
Publication title -
incas buletin
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.282
H-Index - 10
eISSN - 2247-4528
pISSN - 2066-8201
DOI - 10.13111/2066-8201.2022.14.1.15
Subject(s) - partial differential equation , mathematics , numerical partial differential equations , point of delivery , truncation (statistics) , differential equation , first order partial differential equation , proper orthogonal decomposition , scheme (mathematics) , multigrid method , mathematical optimization , mathematical analysis , statistics , agronomy , biology
In this paper we address the subject of mathematical modelling, more precisely the optimization of algorithms for numerically solving partial differential equations. The problem proposed to be tackled in this paper is the implementation of an algorithm for solving partial differential equations in a significantly faster way than that obtained through applying finite difference schemes. The proper orthogonal decomposition (POD) method is a modern and efficient method of reducing the number of variables that occur as a result of applying centred difference schemes to partial differential equations, thus reducing the running time of the algorithm and the accumulation of truncation errors. Therefore, the POD method has been implemented to obtain a reduced order scheme applied to different partial differential equations, with some practical applications and comparisons with the analytical solutions.