An ADI Method for the Numerical Solution of 3D Fractional Reaction-Diffusion Equations

Concezzi, Moreno; Spigler, Renato

doi:10.3390/fractalfract4040057

Cited by 6 publications

(2 citation statements)

References 39 publications

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“…Thus, based on the resulting TIFF format images, specific fractal methods were applied using the Interactive Quantitative Morphology (IQM) 3.5.0 software tool [39]. Fractal textural analysis is an analysis that no longer requires binarization, the method by which quantitative and qualitative elements are lost in most situations and uses grayscale images directly [40]. The textural fractal analysis methods Higuchi 1D (H1D) and Higuchi 2D (H2D) allowed us to quantify the changing complexity of forest patterns.…”

Section: Data and Image Processingmentioning

confidence: 99%

Particularities of Forest Dynamics Using Higuchi Dimension. Parâng Mountains as a Case Study

et al. 2021

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The legal or illegal losses and the natural disturbance regime of forest areas in Romania generate major imbalances in territorial systems. The main purpose of the current research was to examine the dynamics of the complexity of forests under the influence of forest loss but also to compare the applicability of Higuchi dimension. In this study, two fractal algorithms, Higuchi 1D (H1D) and Higuchi 2D (H2D), were used to determine qualitative and quantitative aspects based on images obtained from a Geographic Information System (GIS) database. The H1D analysis showed that the impact of forest loss has led to increased fragmentation of the forests, generating a continuous increase in the complexity of forest areas. The H2D analysis identified the complexity of forest morphology by the relationship between each pixel and the neighboring pixels from analyzed images, which allowed us to highlight the local characteristics of the forest loss. The H1D and H2D methods showed that they have the speed and simplicity required for forest loss analysis. Using this methodology complementary to GIS analyses, a relevant status of how forest loss occurred and their impact on tree-cover dynamics was obtained.

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Section: Data and Image Processingmentioning

confidence: 99%

Particularities of Forest Dynamics Using Higuchi Dimension. Parâng Mountains as a Case Study

et al. 2021

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“…Authors also presented a theorem regarding existence, stability of the presented method, and error estimation with numerical examples. Another interesting study is [16], in which the ADI method to solve fractional reaction-diffusion equations with Dirichlet boundary conditions was described. The authors used a new fractional version of the alternating direction implicit method.…”

Section: Introductionmentioning

confidence: 99%

Computational Methods for Parameter Identification in 2D Fractional System with Riemann–Liouville Derivative

Brociek

Wajda

Sciuto

et al. 2022

Sensors

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In recent times, many different types of systems have been based on fractional derivatives. Thanks to this type of derivatives, it is possible to model certain phenomena in a more precise and desirable way. This article presents a system consisting of a two-dimensional fractional differential equation with the Riemann–Liouville derivative with a numerical algorithm for its solution. The presented algorithm uses the alternating direction implicit method (ADIM). Further, the algorithm for solving the inverse problem consisting of the determination of unknown parameters of the model is also described. For this purpose, the objective function was minimized using the ant algorithm and the Hooke–Jeeves method. Inverse problems with fractional derivatives are important in many engineering applications, such as modeling the phenomenon of anomalous diffusion, designing electrical circuits with a supercapacitor, and application of fractional-order control theory. This paper presents a numerical example illustrating the effectiveness and accuracy of the described methods. The introduction of the example made possible a comparison of the methods of searching for the minimum of the objective function. The presented algorithms can be used as a tool for parameter training in artificial neural networks.

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Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control

Liu

2023

Applied Mathematics and Computation

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An ADI Method for the Numerical Solution of 3D Fractional Reaction-Diffusion Equations

Cited by 6 publications

References 39 publications

Particularities of Forest Dynamics Using Higuchi Dimension. Parâng Mountains as a Case Study

Particularities of Forest Dynamics Using Higuchi Dimension. Parâng Mountains as a Case Study

Computational Methods for Parameter Identification in 2D Fractional System with Riemann–Liouville Derivative

Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control

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