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Inverse differential quadrature method: mathematical formulation and error analysis
Engineering systems are typically governed by systems of high-order differential equations which require efficient numerical methods to provide reliable solutions, subject to imposed constraints. The conventional approach by direct approximation of system variables can potentially incur considerable...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8300657/ https://www.ncbi.nlm.nih.gov/pubmed/35153553 http://dx.doi.org/10.1098/rspa.2020.0815 |
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author | Ojo, Saheed O. Trinh, Luan C. Khalid, Hasan M. Weaver, Paul M. |
author_facet | Ojo, Saheed O. Trinh, Luan C. Khalid, Hasan M. Weaver, Paul M. |
author_sort | Ojo, Saheed O. |
collection | PubMed |
description | Engineering systems are typically governed by systems of high-order differential equations which require efficient numerical methods to provide reliable solutions, subject to imposed constraints. The conventional approach by direct approximation of system variables can potentially incur considerable error due to high sensitivity of high-order numerical differentiation to noise, thus necessitating improved techniques which can better satisfy the requirements of numerical accuracy desirable in solution of high-order systems. To this end, a novel inverse differential quadrature method (iDQM) is proposed for approximation of engineering systems. A detailed formulation of iDQM based on integration and DQM inversion is developed separately for approximation of arbitrary low-order functions from higher derivatives. Error formulation is further developed to evaluate the performance of the proposed method, whereas the accuracy through convergence, robustness and numerical stability is presented through articulation of two unique concepts of the iDQM scheme, known as Mixed iDQM and Full iDQM. By benchmarking iDQM solutions of high-order differential equations of linear and nonlinear systems drawn from heat transfer and mechanics problems against exact and DQM solutions, it is demonstrated that iDQM approximation is robust to furnish accurate solutions without losing computational efficiency, and offer superior numerical stability over DQM solutions. |
format | Online Article Text |
id | pubmed-8300657 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-83006572022-02-11 Inverse differential quadrature method: mathematical formulation and error analysis Ojo, Saheed O. Trinh, Luan C. Khalid, Hasan M. Weaver, Paul M. Proc Math Phys Eng Sci Research Articles Engineering systems are typically governed by systems of high-order differential equations which require efficient numerical methods to provide reliable solutions, subject to imposed constraints. The conventional approach by direct approximation of system variables can potentially incur considerable error due to high sensitivity of high-order numerical differentiation to noise, thus necessitating improved techniques which can better satisfy the requirements of numerical accuracy desirable in solution of high-order systems. To this end, a novel inverse differential quadrature method (iDQM) is proposed for approximation of engineering systems. A detailed formulation of iDQM based on integration and DQM inversion is developed separately for approximation of arbitrary low-order functions from higher derivatives. Error formulation is further developed to evaluate the performance of the proposed method, whereas the accuracy through convergence, robustness and numerical stability is presented through articulation of two unique concepts of the iDQM scheme, known as Mixed iDQM and Full iDQM. By benchmarking iDQM solutions of high-order differential equations of linear and nonlinear systems drawn from heat transfer and mechanics problems against exact and DQM solutions, it is demonstrated that iDQM approximation is robust to furnish accurate solutions without losing computational efficiency, and offer superior numerical stability over DQM solutions. The Royal Society Publishing 2021-04 2021-04-21 /pmc/articles/PMC8300657/ /pubmed/35153553 http://dx.doi.org/10.1098/rspa.2020.0815 Text en © 2021 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Research Articles Ojo, Saheed O. Trinh, Luan C. Khalid, Hasan M. Weaver, Paul M. Inverse differential quadrature method: mathematical formulation and error analysis |
title | Inverse differential quadrature method: mathematical formulation and error analysis |
title_full | Inverse differential quadrature method: mathematical formulation and error analysis |
title_fullStr | Inverse differential quadrature method: mathematical formulation and error analysis |
title_full_unstemmed | Inverse differential quadrature method: mathematical formulation and error analysis |
title_short | Inverse differential quadrature method: mathematical formulation and error analysis |
title_sort | inverse differential quadrature method: mathematical formulation and error analysis |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8300657/ https://www.ncbi.nlm.nih.gov/pubmed/35153553 http://dx.doi.org/10.1098/rspa.2020.0815 |
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