Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations
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DOI: 10.1007/s12190-020-01454-0
Abstract: We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional diffusion equations. Those linear systems are Toeplitz-like. By making… read more here.
Keywords: time dependent; splitting preconditioning; sine transform; riesz space ... 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
Second-order BDF time approximation for Riesz space-fractional diffusion equations
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DOI: 10.1080/00207160.2017.1366461
Abstract: ABSTRACT Second-order backward difference formula (BDF2) is considered for time approximation of Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by the second-order fractional centre difference formula. To improve the computational efficiency, an… read more here.
Keywords: fractional diffusion; space; space fractional; second order ... See more keywords
A Galerkin FEM for Riesz space-fractional CNLS
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DOI: 10.1186/s13662-019-2278-y
Abstract: In quantum physics, fractional Schrödinger equation is of particular interest in the research of particles on stochastic fields modeled by the Lévy processes, which was derived by extending the Feynman path integral over the Brownian… read more here.
Keywords: space fractional; fractional cnls; fem riesz; galerkin fem ... See more keywords