Numerical simulation with the second order compact approximation of first order derivative for the modified fractional diffusion equation

2018 ◽  
Vol 320 ◽  
pp. 319-330 ◽  
Author(s):  
Y. Chen ◽  
Chang-Ming Chen
Keyword(s):  
Numerical Simulation ◽  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Second Order ◽  
Fractional Diffusion Equation ◽  
Order Derivative ◽  
First Order ◽  
Compact Approximation

scholarly journals An inverse problem for a fractional diffusion equation with fractional power type nonlinearities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Li Li
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Approximation Property ◽  
Fractional Power ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Well Posedness ◽  
Power Type ◽  
First Order ◽  
Dirichlet To Neumann Map

<p style='text-indent:20px;'>We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map. Our arguments are based on a first order linearization as well as the parabolic Runge approximation property.</p>

scholarly journals Numerical Solution of Nonstationary Problems for a Space-Fractional Diffusion Equation

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Petr N. Vabishchevich
Keyword(s):  
Diffusion Equation ◽  
Elliptic Operator ◽  
Fractional Power ◽  
Finite Element Approximation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Evolutionary Equation ◽  
Element Approximation ◽  
First Order ◽  
Space Fractional Diffusion Equation

AbstractAn unsteady problem is considered for a space-fractional diffusion equation in abounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. Finite element approximation in space is employed. To construct approximation in time, regularized two-level schemes are used. The numerical implementation is based on solving the equation with the fractional power of the elliptic operator using an auxiliary Cauchy problem for a pseudo-parabolic equation. The results of numerical experiments are presented for a model two-dimensional problem.

Inverse problem for nonlinear backward space-fractional diffusion equation

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Hai Dinh Nguyen Duy ◽  
Tuan Nguyen Huy ◽  
Long Le Dinh ◽  
Gia Quoc Thong Le
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Second Order ◽  
Fractional Diffusion Equation ◽  
Nonlinear Source ◽  
Classical Diffusion ◽  
Space Fractional Diffusion Equation

AbstractIn this paper, a backward diffusion problem for a space-fractional diffusion equation (SFDE) with nonlinear source in a strip is investigated. This problem is obtained from the classical diffusion equation by replacing the second-order space derivative with a Riesz–Feller derivative of order

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