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2024 | OriginalPaper | Chapter

Reconstruction of the Time-Dependent Diffusion Coefficient in a Space-Fractional Parabolic Equation

Authors : Miglena N. Koleva, Lubin G. Vulkov

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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Abstract

We propose two algorithms for investigation the numerical reconstruction of the time-dependent diffusion coefficient in a space-fractional parabolic problem at integral and point measured outputs. In the first one, by implicit Euler method we perform a linearization of the quadratically nonlinear initial boundary value problem on each time level. Then, we apply a decomposition to this problem solution around the unknown diffusion coefficient. Finally, using the integral or point observations we express in exact form by the solutions of the new subproblems, the required diffusion coefficient. By the second one, on each time level, an iterative algorithm based on the secant method for the numerical identification of the diffusion coefficient, is proposed. We compare the two methods on computational test examples.

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previous chapter Impulses in Generalized Proportional Caputo Fractional Differential Equations and Equivalent Integral Presentation
next chapter On the Traveling Wave Solutions of the Fractional Diffusive Predator—Prey System Incorporating an Allee Effect
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Metadata
Title
Reconstruction of the Time-Dependent Diffusion Coefficient in a Space-Fractional Parabolic Equation
Authors
Miglena N. Koleva
Lubin G. Vulkov
Copyright Year
2024
Book
New Trends in the Applications of Differential Equations in Sciences

Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-53212-2_23

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