Application of nonlinear time-fractional partial differential equations to image processing via hybrid Laplace transform method
type: Item
instance of: scholarly article
title: Application of nonlinear time-fractional partial differential equations to image processing via hybrid Laplace transform method
zbMATH Open document ID: 1487.35405
DOI: 10.1155/2018/8924547
author: Xianqiang Yang
published in: Journal of Mathematics
publication date: 2019-02-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35Q94
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 7029805
describes a project that uses: NDSolve
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8924547
OpenAlex ID: W2889690622
cites work: Two hybrid methods for solving two-dimensional linear time-fractional partial differential equations
cites work: A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Q3864730
cites work: Solution for a fractional diffusion-wave equation defined in a bounded domain
cites work: An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein-Gordon equations in fluid mechanics
cites work: Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation
cites work: Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
cites work: Image Processing through Reaction Combined with Nonlinear Diffusion
cites work: Solution of nonlinear diffusion appearing in image smoothing and edge detection
cites work: Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II
cites work: On some applications of diffusion processes for image processing
cites work: A novel approach to text binarization via a diffusion-based model
cites work: A locally adaptive, diffusion based text binarization technique
cites work: Parabolic and hyperbolic contours for computing the Bromwich integral
cites work: Unsteady mixed convection from a rotating vertical slender cylinder in an axial flow
cites work: Unsteady mixed convection flow over a vertical stretching sheet in a parallel free stream with variable wall temperature
cites work: Unsteady mixed convection flow from a moving vertical plate in a parallel free stream: Influence of heat generation or absorption
cites work: Roundoff error in computing derivatives using the Chebyshev differentiation matrix
cites work: Accuracy and Speed in Computing the Chebyshev Collocation Derivative
cites work: On the errors incurred calculating derivatives using Chebyshev polynomials
Wikidata QID: Q129221620
Recommended article: Spectral approximation of fractional PDEs in image processing and phase field modeling
Recommended article: A simple and flexible modification of Grünwald-Letnikov fractional derivative in image processing
Recommended article: A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition
Recommended article: Q3651365
Recommended article: Q4641265
Recommended article: Fractional calculus in image processing: a review
Recommended article: On an inverse problem of nonlinear imaging with fractional damping
Recommended article: Finite difference and Legendre spectral method for a time-fractional diffusion-convection equation for image restoration
Recommended article: Q3621589
Recommended article: On a fractional reaction-diffusion system applied to image decomposition and restoration
description: scientific article; zbMATH DE number 7029805