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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...

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Detalles Bibliográficos
Autores principales: Ojo, Saheed O., Trinh, Luan C., Khalid, Hasan M., Weaver, Paul M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2021
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.
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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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