Application of Nonlinear Time-Fractional Partial Differential Equations to Image Processing via Hybrid Laplace Transform Method
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 tempo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/8924547 |
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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |