A unified view of some numerical methods for fractional diffusion

DOI10.1016/j.camwa.2019.07.025zbMath1446.65153OpenAlexW2966527466WikidataQ127408021 ScholiaQ127408021MaRDI QIDQ2192559

Clemens Hofreither

Publication date: 17 August 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2019.07.025

zbMATH Keywords

numerical methodsrational approximationfractional diffusionfractional Laplace

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Fractional derivatives and integrals (26A33) Approximation by rational functions (41A20) Laplace transform (44A10) Multilinear algebra, tensor calculus (15A69) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Fractional partial differential equations (35R11)

Related Items (21)

A Newton's method for best uniform polynomial approximation ⋮ Reduced sum implementation of the BURA method for spectral fractional diffusion problems ⋮ Factorized schemes for first and second order evolution equations with fractional powers of operators ⋮ Exponentially convergent trapezoidal rules to approximate fractional powers of operators ⋮ A survey on numerical methods for spectral space-fractional diffusion problems ⋮ Neumann fractional diffusion problems: BURA solution methods and algorithms ⋮ On rational Krylov and reduced basis methods for fractional diffusion ⋮ Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons ⋮ Rational approximation preconditioners for multiphysics problems ⋮ Fractional exponential fitting backward differential formulas for solving differential equations of fractional order ⋮ NUMERICAL SIMULATION OF FRACTIONAL POWER DIFFUSION BIOSENSORS ⋮ A Newton method for best uniform rational approximation ⋮ Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation ⋮ A Gaussian method for the square root of accretive operators ⋮ Double exponential quadrature for fractional diffusion ⋮ An a posteriori error estimator for the spectral fractional power of the Laplacian ⋮ Parallel BURA Based Numerical Solution of Fractional Laplacian with Pure Neumann Boundary Conditions ⋮ High-Order Two and Three Level Schemes for Solving Fractional Powers of Elliptic Operators ⋮ Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator ⋮ An algorithm for best rational approximation based on barycentric rational interpolation ⋮ A reduced basis method for fractional diffusion operators. II

Uses Software

• DLMF
• Chebfun
• AAA

Cites Work

• Unnamed Item
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• Numerical methods for fractional diffusion

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