DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation
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DOI: 10.1007/s10915-017-0369-z
Abstract: We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test functions and show… read more here.
Keywords: optimal test; advection diffusion; fractional advection; test functions ... See more keywords
A numerical method for a time-fractional advection–dispersion equation with a nonlinear source term
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-019-01266-x
Abstract: In this paper we propose an implicit finite-difference scheme to approximate the solution of an initial-boundary value problem for a time-fractional advection–dispersion equation with variable coefficients and a nonlinear source term. The time fractional derivative… read more here.
Keywords: time; advection dispersion; fractional advection; dispersion equation ... See more keywords
Numerical treatment of the space fractional advection–dispersion model arising in groundwater hydrology
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DOI: 10.1007/s40314-020-01410-5
Abstract: This paper studies a new computational method for the approximate solution of the space fractional advection–dispersion equation in sense of Caputo derivatives. In the first method, a time discretization is accomplished via the compact finite… read more here.
Keywords: space fractional; advection dispersion; hydrology; fractional advection ... See more keywords
Numerical approximations for the Riesz space fractional advection-dispersion equations via radial basis functions
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DOI: 10.1016/j.apnum.2019.05.011
Abstract: Abstract The radial basis functions collocation method is developed to solve Riesz space fractional advection-dispersion equation (RSFADE). To do this, we first provide the Riemann-Liouville fractional derivatives of the five kinds of RBFs, including the… read more here.
Keywords: basis functions; fractional advection; space; riesz space ... See more keywords
Carleman estimates for the time-fractional advection-diffusion equations and applications
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DOI: 10.1088/1361-6420/ab0138
Abstract: In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the first order time-derivative. As a direct application of the Carleman estimates, we show… read more here.
Keywords: carleman estimates; time fractional; fractional advection; advection diffusion ... See more keywords
On Numerical Solution Of The Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu-Caputo Derivative
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DOI: 10.1515/phys-2019-0085
Abstract: Abstract A powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): A B C D 0 + , t β u ( x , t ) = ζ u x… read more here.
Keywords: equation; advection diffusion; time fractional; fractional advection ... See more keywords
Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation
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DOI: 10.3390/e19070297
Abstract: Two approaches resulting in two different generalizations of the space-time-fractional advection-diffusion equation are discussed. The Caputo time-fractional derivative and Riesz fractional Laplacian are used. The fundamental solutions to the corresponding Cauchy and source problems in… read more here.
Keywords: two approaches; advection diffusion; time fractional; fractional advection ... See more keywords