High-order solvers for space-fractional differential equations with Riesz derivative

DOI10.3934/dcdss.2019037zbMath1422.65179OpenAlexW2890666733WikidataQ129227520 ScholiaQ129227520MaRDI QIDQ2319607

Kolade M. Owolabi, Abdon Atangana

Publication date: 20 August 2019

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2019037

zbMATH Keywords

finite differencenumerical simulationsRiesz derivativeimplicit-explicitfractional nonlinear PDEsETD method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Fractional partial differential equations (35R11)

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Uses Software

• RODAS

Cites Work

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• Higher-order time-stepping methods for time-dependent reaction-diffusion equations arising in biology
• A Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equations
• A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
• Fourier spectral methods for fractional-in-space reaction-diffusion equations
• Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order
• Controlling the wave movement on the surface of shallow water with the Caputo-Fabrizio derivative with fractional order
• Chua's circuit model with Atangana-Baleanu derivative with fractional order
• Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model
• Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
• On the fractional signals and systems
• Fractional calculus for scientists and engineers.
• Implicit-explicit predictor-corrector schemes for nonlinear parabolic differential equations
• Exponential time differencing for stiff systems
• Fractional calculus in viscoelasticity: an experimental study
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Fractional calculus models of complex dynamics in biological tissues
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Mathematical biology. Vol. 1: An introduction.
• Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation
• Robust IMEX schemes for solving two-dimensional reaction-diffusion models
• Fox \(H\) functions in fractional diffusion
• Implicit-explicit multistep methods for quasilinear parabolic equations
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• The differentiability in the fractional calculus.
• Finite difference approximations for fractional advection-dispersion flow equations
• Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order
• Fourier spectral method for higher order space fractional reaction-diffusion equations
• The locally extrapolated exponential time differencing LOD scheme for multidimensional reaction-diffusion systems
• Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems
• IMEX Runge-Kutta schemes for reaction-diffusion equations
• Analysis and applications of the exponential time differencing schemes and their contour integration modifications
• Finite difference methods for two-dimensional fractional dispersion equation
• Analysis of the heterogeneous multiscale method for ordinary differential equations
• Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer
• Mathematical study of two-variable systems with adaptive numerical methods
• Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
• Elements of Mathematical Ecology
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Fractional differentiation matrices with applications
• Advances in Fractional Calculus
• Fourth-Order Time-Stepping for Stiff PDEs
• Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations
• Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• A real distinct poles exponential time differencing scheme for reaction-diffusion systems
• A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation