A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation

In this article, a hybrid Haar wavelet collocation method (HWCM) is proposed for the ill-posed inverse problem with unknown source control parameters. Applying numerical techniques to such problems is a challenging task due to the presence of nonlinear terms, unknown control parameter sources along...

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Autores principales:	Ahsan Muhammad, Lin Shanwei, Ahmad Masood, Nisar Muhammad, Ahmad Imtiaz, Ahmed Hijaz, Liu Xuan
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	nonlinear ill-posed pde haar wavelets stability condition number Physics QC1-999
Acceso en línea:	https://doaj.org/article/3df1714c534a4530bc344dee9c033d20
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id	oai:doaj.org-article:3df1714c534a4530bc344dee9c033d20
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spelling	oai:doaj.org-article:3df1714c534a4530bc344dee9c033d202021-12-05T14:11:02ZA Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation2391-547110.1515/phys-2021-0080https://doaj.org/article/3df1714c534a4530bc344dee9c033d202021-11-01T00:00:00Zhttps://doi.org/10.1515/phys-2021-0080https://doaj.org/toc/2391-5471In this article, a hybrid Haar wavelet collocation method (HWCM) is proposed for the ill-posed inverse problem with unknown source control parameters. Applying numerical techniques to such problems is a challenging task due to the presence of nonlinear terms, unknown control parameter sources along the solution inside the given region. To find the numerical solution, derivatives are discretized adopting implicit finite-difference scheme and Haar wavelets. The computational stability and theoretical rate of convergence of the proposed HWCM are discussed in detail. Two numerical experiments are incorporated to show the well-condition behavior of the matrix obtained from HWCM and hence not required to supplement some regularization procedures. Moreover, the numerical solutions of the considered experiments illustrate the reliability, suitability, and correctness of HWCM.Ahsan MuhammadLin ShanweiAhmad MasoodNisar MuhammadAhmad ImtiazAhmed HijazLiu XuanDe Gruyterarticlenonlinear ill-posed pdehaar waveletsstabilitycondition numberPhysicsQC1-999ENOpen Physics, Vol 19, Iss 1, Pp 722-734 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonlinear ill-posed pde haar wavelets stability condition number Physics QC1-999
spellingShingle	nonlinear ill-posed pde haar wavelets stability condition number Physics QC1-999 Ahsan Muhammad Lin Shanwei Ahmad Masood Nisar Muhammad Ahmad Imtiaz Ahmed Hijaz Liu Xuan A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
description	In this article, a hybrid Haar wavelet collocation method (HWCM) is proposed for the ill-posed inverse problem with unknown source control parameters. Applying numerical techniques to such problems is a challenging task due to the presence of nonlinear terms, unknown control parameter sources along the solution inside the given region. To find the numerical solution, derivatives are discretized adopting implicit finite-difference scheme and Haar wavelets. The computational stability and theoretical rate of convergence of the proposed HWCM are discussed in detail. Two numerical experiments are incorporated to show the well-condition behavior of the matrix obtained from HWCM and hence not required to supplement some regularization procedures. Moreover, the numerical solutions of the considered experiments illustrate the reliability, suitability, and correctness of HWCM.
format	article
author	Ahsan Muhammad Lin Shanwei Ahmad Masood Nisar Muhammad Ahmad Imtiaz Ahmed Hijaz Liu Xuan
author_facet	Ahsan Muhammad Lin Shanwei Ahmad Masood Nisar Muhammad Ahmad Imtiaz Ahmed Hijaz Liu Xuan
author_sort	Ahsan Muhammad
title	A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
title_short	A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
title_full	A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
title_fullStr	A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
title_full_unstemmed	A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
title_sort	haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/3df1714c534a4530bc344dee9c033d20
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A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation

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