The space-fractional diffusion-advection equation: analytical solutions and critical assessment of numerical solutions

DOI10.2478/S13540-014-0161-9zbMath1312.35188arXiv1309.4263OpenAlexW3105793960MaRDI QIDQ2347401

Frederic Effenberger, Robin Stern, Horst Fichtner, Tobias Schäfer

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4263

zbMATH Keywords

anomalous diffusionnumerical approximationsRiesz fractional derivativeseries representation of analytical solutionsspace-fractional diffusion-advection equation

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Diffusion processes (60J60) PDEs with randomness, stochastic partial differential equations (35R60) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Fractional partial differential equations (35R11)

Related Items (17)

General solution of a fractional diffusion-advection equation for solar cosmic-ray transport ⋮ Time-space fractional derivative models for \(\text{CO}_{2}\) transport in heterogeneous media ⋮ Analytical solution of the space-time fractional hyperdiffusion equation ⋮ On the fractional diffusion-advection-reaction equation in \(\mathbb{R}\) ⋮ New solution of diffusion-advection equation for cosmic-ray transport using ultradistributions ⋮ On solving fractional logistic population models with applications ⋮ An analytical study of fractional Klein-Kramers approximations for describing anomalous diffusion of energetic particles ⋮ Fundamental solutions to advection-diffusion equation with time-fractional Caputo-Fabrizio derivative ⋮ General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation ⋮ Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms ⋮ An advanced numerical modeling for Riesz space fractional advection-dispersion equations by a meshfree approach ⋮ An algorithm for the approximate solution of the fractional Riccati differential equation ⋮ Numerical approximations for the Riesz space fractional advection-dispersion equations via radial basis functions ⋮ Thermal blow-up in a finite strip with superdiffusive properties ⋮ Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain ⋮ Numerical solution of nonstationary problems for a space-fractional diffusion equation ⋮ Solving 3D time-fractional diffusion equations by high-performance parallel computing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A second order explicit finite difference method for the fractional advection diffusion equation
• Anomalous is ubiquitous
• A second-order accurate numerical method for the two-dimensional fractional diffusion equation
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Approximation of Lévy-Feller diffusion by random walk
• Fox \(H\) functions in fractional diffusion
• Finite difference approximations for fractional advection-dispersion flow equations
• A stochastic differential equation code for multidimensional Fokker-Planck type problems
• SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equations
• On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion
• Finite difference approximations for two-sided space-fractional partial differential equations
• Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations
• Fronts in anomalous diffusion–reaction systems
• A Method for Simulating Stable Random Variables
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: The space-fractional diffusion-advection equation: analytical solutions and critical assessment of numerical solutions