Efficient implementation of rational approximations to fractional differential operators

DOI10.1007/s10915-017-0633-2zbMath1398.65089OpenAlexW2776599320MaRDI QIDQ1668740

Paolo Novati, Lidia Aceto

Publication date: 29 August 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-017-0633-2

zbMATH Keywords

Padé approximantsmatrix functionsCaputo fractional derivativefractional Laplacian operatorGauss-Jacobi rule

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation, An approximate representation of a solution to fractional elliptical BVP via solution of parabolic IVP, A survey on numerical methods for spectral space-fractional diffusion problems, Padé-type approximations to the resolvent of fractional powers of operators, A rational preconditioner for multi-dimensional Riesz fractional diffusion equations, Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis, Rational Krylov methods for functions of matrices with applications to fractional partial differential equations, A numerical study of fractional linear algebraic systems, Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator, Rational approximations to fractional powers of self-adjoint positive operators

Uses Software

• FastGaussQuadrature
• ma2dfc
• mftoolbox

Cites Work

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