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Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods

This research work deals with two spectral matrix collocation algorithms based on (novel) clique functions to solve two classes of nonlinear nonlocal elliptic two-points boundary value problems (BVPs) arising in diverse physical models. The nonlinearity together with nonlocality makes the models so...

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Detalles Bibliográficos
Autores principales: Izadi, Mohammad, Singh, Jagdev, Noeiaghdam, Samad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10694310/
http://dx.doi.org/10.1016/j.heliyon.2023.e22267
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author Izadi, Mohammad
Singh, Jagdev
Noeiaghdam, Samad
author_facet Izadi, Mohammad
Singh, Jagdev
Noeiaghdam, Samad
author_sort Izadi, Mohammad
collection PubMed
description This research work deals with two spectral matrix collocation algorithms based on (novel) clique functions to solve two classes of nonlinear nonlocal elliptic two-points boundary value problems (BVPs) arising in diverse physical models. The nonlinearity together with nonlocality makes the models so difficult to solve numerically. In both matrix methods by expanding the unknown solutions in terms of clique polynomials the nonlocality in the models is handled. In the first and direct technique, the clique coefficients are determined in an accurate way through solving an algebraic system of nonlinear equations. To get rid of the nonlinearity of the models and in order to gain efficacy, the quasilinearization method (QLM) is utilized in the second approach. In the latter algorithm named QLM-clique procedure, the first directly clique collocation method is applied to a family of linearized equations in an iterative manner. In particular, we show that the series expansion of clique polynomials is convergent exponentially in a weighted [Formula: see text] norm. Numerous numerical simulations validate the performance of two matrix collocation schemes and demonstrate the accuracy as well as the gain in computational efficiency in terms of elapsed CPU time. The proposed matrix algorithms for computation are easy to implement and straightforward, and provide more accuracy compared to other available computational values in the literature.
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spelling pubmed-106943102023-12-05 Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods Izadi, Mohammad Singh, Jagdev Noeiaghdam, Samad Heliyon Research Article This research work deals with two spectral matrix collocation algorithms based on (novel) clique functions to solve two classes of nonlinear nonlocal elliptic two-points boundary value problems (BVPs) arising in diverse physical models. The nonlinearity together with nonlocality makes the models so difficult to solve numerically. In both matrix methods by expanding the unknown solutions in terms of clique polynomials the nonlocality in the models is handled. In the first and direct technique, the clique coefficients are determined in an accurate way through solving an algebraic system of nonlinear equations. To get rid of the nonlinearity of the models and in order to gain efficacy, the quasilinearization method (QLM) is utilized in the second approach. In the latter algorithm named QLM-clique procedure, the first directly clique collocation method is applied to a family of linearized equations in an iterative manner. In particular, we show that the series expansion of clique polynomials is convergent exponentially in a weighted [Formula: see text] norm. Numerous numerical simulations validate the performance of two matrix collocation schemes and demonstrate the accuracy as well as the gain in computational efficiency in terms of elapsed CPU time. The proposed matrix algorithms for computation are easy to implement and straightforward, and provide more accuracy compared to other available computational values in the literature. Elsevier 2023-11-13 /pmc/articles/PMC10694310/ http://dx.doi.org/10.1016/j.heliyon.2023.e22267 Text en © 2023 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
Izadi, Mohammad
Singh, Jagdev
Noeiaghdam, Samad
Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods
title Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods
title_full Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods
title_fullStr Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods
title_full_unstemmed Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods
title_short Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods
title_sort simulating accurate and effective solutions of some nonlinear nonlocal two-point bvps: clique and qlm-clique matrix methods
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10694310/
http://dx.doi.org/10.1016/j.heliyon.2023.e22267
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