Determination of time-dependent coefficients in moving boundary problems under nonlocal and heat moment observations
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Publication Date
Tue May 01 2012
Journal Name
Engineering Analysis With Boundary Elements
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Publication Date
Fri Mar 29 2024
Journal Name
Iraqi Journal Of Science
Determination of Timewise-Source Coefficient in Time-Fractional Reaction-Diffusion Equation from First Order Heat Moment
This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie
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Publication Date
Thu Feb 01 2018
Journal Name
Applied Mathematical Modelling
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Publication Date
Mon Oct 01 2012
Journal Name
Computers & Mathematics With Applications
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Publication Date
Mon Jan 01 2024
Journal Name
2nd International Conference For Engineering Sciences And Information Technology (esit 2022): Esit2022 Conference Proceedings
Publication Date
Thu Dec 01 2011
Journal Name
Engineering Analysis With Boundary Elements
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Publication Date
Thu Apr 27 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Numerical Solutions Of The Nonlocal Problems For The Diffusion Partial Differential Equations
finite difference method
implicit finite difference method
explicit finite difference method
nonlocal condition
diffusion equation.
In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.
Publication Date
Mon Jan 01 2024
Journal Name
2nd International Conference For Engineering Sciences And Information Technology (esit 2022): Esit2022 Conference Proceedings
Publication Date
Fri Nov 01 2013
Journal Name
East Asian Journal On Applied Mathematics
Free Boundary Determination in Nonlinear Diffusion
Abstract<p>Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the <italic>lsqnonlin</italic> routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, inst</p>
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Publication Date
Wed Jan 01 2020
Journal Name
Arab Journal Of Basic And Applied Sciences
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