Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method

B. A. Jacobs and C. Harley

Journal of Mathematics, 2018, vol. 2018, 1-9

Abstract:

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8924547

DOI: 10.1155/2018/8924547

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