Simultaneous determination of time and space-dependent coefficients in a parabolic equation
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Publication Date
Sat Mar 01 2014
Journal Name
Computers & Mathematics With Applications
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Publication Date
Tue Feb 10 2026
Journal Name
F1000research
Simultaneous Numerical Determination of Two Time-dependent Coefficients in Second Order Parabolic Equation With Nonlocal Initial and Boundary Conditions
Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine
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Publication Date
Fri Oct 14 2016
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Thu Dec 21 2023
Journal Name
Mathematical Modelling Of Engineering Problems
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Publication Date
Thu Jun 01 2023
Journal Name
Partial Differential Equations In Applied Mathematics
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Publication Date
Thu Jan 01 2015
Journal Name
Finite Difference Methods,theory And Applications
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Publication Date
Tue Mar 16 2021
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Thu Dec 18 2025
Journal Name
Mathematical Methods In The Applied Sciences
Time‐Dependent Term Identification in the Time–Space Fractional Derivative Diffusion Equation From Integral Over Specified Condition
ABSTRACT<p>
In this paper, a time–space fractional order inverse source problem to determine the temperature solution and the time‐dependent source term from heat moment to the time–space fractional heat equation with an initial condition, homogeneous Dirichlet boundary conditions, and integral overdetermination condition is investigated. Two unconditionally stable finite difference schemes are proposed to find a numerical solution of the direct problem. Namely, method I is based on the approximation of the time‐fractional derivative via Laplace transformation, whereas method II is based on finite difference approximation. The inverse problem is solved iteratively </p>
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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
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Publication Date
Mon May 01 2017
Journal Name
Applied Mathematics And Computation
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