Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method
Joint Authors
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-17
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
This work considers a hybrid solution method for the time-fractional diffusion model with a cubic nonlinear source term in one and two dimensions.
Both Dirichlet and Neumann boundary conditions are considered for each dimensional case.
The hybrid method involves a Laplace transformation in the temporal domain which is numerically inverted, and Chebyshev collocation is employed in the spatial domain due to its increased accuracy over a standard finite-difference discretization.
Due to the fractional-order derivative we are only able to compare the accuracy of this method with Mathematica’s NDSolve in the case of integer derivatives; however, a detailed discussion of the merits and shortcomings of the proposed hybridization is presented.
An application to image processing via a finite-difference discretization is included in order to substantiate the application of this method.
American Psychological Association (APA)
Jacobs, B. A.& Harley, Charis. 2018. Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method. Journal of Mathematics،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1193597
Modern Language Association (MLA)
Jacobs, B. A.& Harley, Charis. Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method. Journal of Mathematics No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1193597
American Medical Association (AMA)
Jacobs, B. A.& Harley, Charis. Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method. Journal of Mathematics. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1193597
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193597