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Recovering Time-Dependent Coefficients in a Two-Dimensional Parabolic Equation Using Nonlocal Overspecified Conditions via ADE Finite Difference Schemes

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Publication Date
Fri Apr 01 2016
Journal Name
Communications In Nonlinear Science And Numerical Simulation
Simultaneous determination of time and space-dependent coefficients in a parabolic equation

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Publication Date
Mon May 15 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Finite Difference Method for Two-Dimensional Fractional Partial Differential Equation with parameter

 In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.

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Publication Date
Wed Mar 30 2022
Journal Name
Iraqi Journal Of Science
Retrieval of Timewise Coefficients in the Heat Equation from Nonlocal Overdetermination Conditions

     This paper investigates the simultaneous recovery for two time-dependent coefficients for heat equation under Neumann boundary condition. This problem is considered under extra conditions of nonlocal type. The main issue with this problem is the solution unstable to small contamination of noise in the input data. The Crank-Nicolson finite difference method is utilized to solve the direct problem whilst the inverse problem is viewed as nonlinear optimization problem. The later problem is solved numerically using optimization toolbox from MATLAB. We found that the numerical results are accurate and stable.

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Numerical Approximations of a One-Dimensional Time-Fractional Semilinear Parabolic Equation

     The time fractional order differential equations are fundamental tools that are used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order  where , in the standard equation with the Caputo fractional formula. In this paper, two implicit difference schemes: the linearly Euler implicit and the Crank-Nicolson (CN) finite difference schemes, are employed in solving a one-dimensional time-fractional semilinear equation with Dirichlet boundary conditions. Moreover, the consistency, stability and convergence of the proposed schemes are investigated. We prove that the IEM is unconditionally stable, while CNM is conditionally stable. Furthermore, a comparative study between these two s

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Publication Date
Sat Mar 01 2014
Journal Name
Computers & Mathematics With Applications
Simultaneous determination of time-dependent coefficients in the heat equation

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Publication Date
Tue Mar 30 2021
Journal Name
Iraqi Journal Of Science
Numerical Solution to Recover Time-dependent Coefficient and Free Boundary from Nonlocal and Stefan Type Overdetermination Conditions in Heat Equation

This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via

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Publication Date
Tue Mar 16 2021
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
Determination of time-dependent coefficients in moving boundary problems under nonlocal and heat moment observations

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Publication Date
Mon Jan 30 2023
Journal Name
Iraqi Journal Of Science
Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term

  This paper deals with numerical approximations of a one-dimensional semilinear parabolic equation with a gradient term. Firstly, we derive the semidiscrete problem of the considered problem and discuss its convergence and blow-up properties. Secondly, we propose both Euler explicit and implicit finite differences methods with a non-fixed time-stepping procedure to estimate the numerical blow-up time of the considered problem. Finally, two numerical experiments are given to illustrate the efficiency, accuracy, and numerical order of convergence of the proposed schemes.

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Publication Date
Mon Jun 22 2020
Journal Name
Baghdad Science Journal
Splitting the One-Dimensional Wave Equation. Part I: Solving by Finite-Difference Method and Separation Variables

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

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Publication Date
Tue May 30 2023
Journal Name
Iraqi Journal Of Science
Reconstruction of Timewise Dependent Coefficient and Free Boundary in Nonlocal Diffusion Equation with Stefan and Heat Flux as Overdetermination Conditions

     The problem of reconstruction of a timewise dependent coefficient and free boundary at once in a nonlocal diffusion equation under Stefan and heat Flux as nonlocal overdetermination conditions have been considered. A Crank–Nicolson finite difference method (FDM) combined with the trapezoidal rule quadrature is used for the direct problem. While the inverse problem is reformulated as a nonlinear regularized least-square optimization problem with simple bound and solved efficiently by MATLAB subroutine lsqnonlin from the optimization toolbox. Since the problem under investigation is generally ill-posed, a small error in the input data leads to a huge error in the output, then Tikhonov’s regularization technique is app

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