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Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method
In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, in...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8327671/ https://www.ncbi.nlm.nih.gov/pubmed/34377855 http://dx.doi.org/10.1016/j.heliyon.2021.e07600 |
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author | Ahmad, Iftikhar Ilyas, Hira Kutlu, Kadir Anam, Vizda Hussain, Syed Ibrar Guirao, Juan Luis García |
author_facet | Ahmad, Iftikhar Ilyas, Hira Kutlu, Kadir Anam, Vizda Hussain, Syed Ibrar Guirao, Juan Luis García |
author_sort | Ahmad, Iftikhar |
collection | PubMed |
description | In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, interfaces, and integrated biological applications in mesophase materials and processes. Sinc functions provide the procedure for function approximation over all types of domains containing singularities, semi-infinite or infinite domains. Sinc functions have been used to reduce HSE into an algebraic system of equations that makes the solution quite superficial. These algebraic equations have been interpreted as matrices. This projected that sinc collocation technique is considerably efficacious on computational ground for higher accuracy and convergence of numerical solutions. Stability analysis of the proposed technique has ensured the accuracy and reliability of the method, moreover, as the stability parameter satisfied the condition the proposed solution of the problem converges. The solution of the HSE is presented through graphical figures and tables for different cases that are constructed on various values of θ and collocation points. The accuracy and efficiency of the proposed technique is analyzed on the basis of absolute errors. |
format | Online Article Text |
id | pubmed-8327671 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Elsevier |
record_format | MEDLINE/PubMed |
spelling | pubmed-83276712021-08-09 Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method Ahmad, Iftikhar Ilyas, Hira Kutlu, Kadir Anam, Vizda Hussain, Syed Ibrar Guirao, Juan Luis García Heliyon Research Article In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, interfaces, and integrated biological applications in mesophase materials and processes. Sinc functions provide the procedure for function approximation over all types of domains containing singularities, semi-infinite or infinite domains. Sinc functions have been used to reduce HSE into an algebraic system of equations that makes the solution quite superficial. These algebraic equations have been interpreted as matrices. This projected that sinc collocation technique is considerably efficacious on computational ground for higher accuracy and convergence of numerical solutions. Stability analysis of the proposed technique has ensured the accuracy and reliability of the method, moreover, as the stability parameter satisfied the condition the proposed solution of the problem converges. The solution of the HSE is presented through graphical figures and tables for different cases that are constructed on various values of θ and collocation points. The accuracy and efficiency of the proposed technique is analyzed on the basis of absolute errors. Elsevier 2021-07-21 /pmc/articles/PMC8327671/ /pubmed/34377855 http://dx.doi.org/10.1016/j.heliyon.2021.e07600 Text en © 2021 The Author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). |
spellingShingle | Research Article Ahmad, Iftikhar Ilyas, Hira Kutlu, Kadir Anam, Vizda Hussain, Syed Ibrar Guirao, Juan Luis García Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method |
title | Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method |
title_full | Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method |
title_fullStr | Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method |
title_full_unstemmed | Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method |
title_short | Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method |
title_sort | numerical computing approach for solving hunter-saxton equation arising in liquid crystal model through sinc collocation method |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8327671/ https://www.ncbi.nlm.nih.gov/pubmed/34377855 http://dx.doi.org/10.1016/j.heliyon.2021.e07600 |
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