A time-space spectral tau method for the time fractional cable equation and its inverse problem

DOI10.1016/j.apnum.2018.03.016zbMath1393.65036OpenAlexW2795780542MaRDI QIDQ1748423

Hui Zhang, Xiu Yang, Xiao-yun Jiang

Publication date: 11 May 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.03.016

zbMATH Keywords

parameter estimationnonlinear conjugate gradient methodCaputo fractional derivativetime fractional cable equationtime-space spectral Legendre tau method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Fractional derivatives and integrals (26A33) Inverse problems for PDEs (35R30) Iterative numerical methods for linear systems (65F10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items

Galerkin operational approach for multi-dimensions fractional differential equations ⋮ A numerical study of anomalous electro-diffusion cells in cable sense with a non-singular kernel ⋮ Approximate solution of the multi-term time fractional diffusion and diffusion-wave equations ⋮ Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications ⋮ Numerical solution for solving fractional parabolic partial differential equations ⋮ Finite element methods based on two families of second-order numerical formulas for the fractional cable model with smooth solutions ⋮ Local discontinuous Galerkin method combined with the \(L2\) formula for the time fractional cable model

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