Space-dependent heat source determination problem with nonlocal periodic boundary conditions

The purpose of this paper is to identify the space-dependent heat source coefficient numerically, for the first time, in the third-order pseudo-parabolic equation with initial and nonlocal periodic boundary conditions from nonlocal integral observation. This problem emerges significantly in the mode...

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Autor principal:	M.J. Huntul
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Pseudo-parabolic equation Inverse source problem Nonlocal periodic boundary Stability analysis Tikhonov regularization Nonlinear optimization Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4313c511142544e0a5e7e3c56733f6d6
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spelling	oai:doaj.org-article:4313c511142544e0a5e7e3c56733f6d62021-11-22T04:29:25ZSpace-dependent heat source determination problem with nonlocal periodic boundary conditions2590-037410.1016/j.rinam.2021.100223https://doaj.org/article/4313c511142544e0a5e7e3c56733f6d62021-11-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2590037421000546https://doaj.org/toc/2590-0374The purpose of this paper is to identify the space-dependent heat source coefficient numerically, for the first time, in the third-order pseudo-parabolic equation with initial and nonlocal periodic boundary conditions from nonlocal integral observation. This problem emerges significantly in the modelling of numerous phenomena in physics, engineering, mechanics and science. Although, the inverse source problem considered in this article is ill-posed by being sensitive to noise but has a unique solution. For the numerical realization, we apply the finite difference method (FDM) for discretizing the forward problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB subroutine lsqnonlin. Numerical results presented for two benchmark test examples with linear and nonlinear source functions show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data. Furthermore, the von Neumann stability analysis is also discussed.M.J. HuntulElsevierarticlePseudo-parabolic equationInverse source problemNonlocal periodic boundaryStability analysisTikhonov regularizationNonlinear optimizationMathematicsQA1-939ENResults in Applied Mathematics, Vol 12, Iss , Pp 100223- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Pseudo-parabolic equation Inverse source problem Nonlocal periodic boundary Stability analysis Tikhonov regularization Nonlinear optimization Mathematics QA1-939
spellingShingle	Pseudo-parabolic equation Inverse source problem Nonlocal periodic boundary Stability analysis Tikhonov regularization Nonlinear optimization Mathematics QA1-939 M.J. Huntul Space-dependent heat source determination problem with nonlocal periodic boundary conditions
description	The purpose of this paper is to identify the space-dependent heat source coefficient numerically, for the first time, in the third-order pseudo-parabolic equation with initial and nonlocal periodic boundary conditions from nonlocal integral observation. This problem emerges significantly in the modelling of numerous phenomena in physics, engineering, mechanics and science. Although, the inverse source problem considered in this article is ill-posed by being sensitive to noise but has a unique solution. For the numerical realization, we apply the finite difference method (FDM) for discretizing the forward problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB subroutine lsqnonlin. Numerical results presented for two benchmark test examples with linear and nonlinear source functions show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data. Furthermore, the von Neumann stability analysis is also discussed.
format	article
author	M.J. Huntul
author_facet	M.J. Huntul
author_sort	M.J. Huntul
title	Space-dependent heat source determination problem with nonlocal periodic boundary conditions
title_short	Space-dependent heat source determination problem with nonlocal periodic boundary conditions
title_full	Space-dependent heat source determination problem with nonlocal periodic boundary conditions
title_fullStr	Space-dependent heat source determination problem with nonlocal periodic boundary conditions
title_full_unstemmed	Space-dependent heat source determination problem with nonlocal periodic boundary conditions
title_sort	space-dependent heat source determination problem with nonlocal periodic boundary conditions
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/4313c511142544e0a5e7e3c56733f6d6
work_keys_str_mv	AT mjhuntul spacedependentheatsourcedeterminationproblemwithnonlocalperiodicboundaryconditions
_version_	1718418156502908928

Space-dependent heat source determination problem with nonlocal periodic boundary conditions

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