On the time-fractional Schrödinger equation: theoretical analysis and numerical solution by matrix Mittag-Leffler functions

DOI10.1016/j.camwa.2016.11.028zbMath1448.65099OpenAlexW2565756501MaRDI QIDQ1643250

Roberto Garrappa, Marina Popolizio, Igor Moret

Publication date: 19 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.11.028

zbMATH Keywords

Mittag-Leffler functionconvergenceKrylov subspace methodstime-fractional Schrödinger equationshift-and-invert

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10) Mittag-Leffler functions and generalizations (33E12) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (15)

Uniquely identifying the variable order of time-fractional partial differential equations on general multi-dimensional domains ⋮ Computing the matrix Mittag-Leffler function with applications to fractional calculus ⋮ Numerical solution of multiterm fractional differential equations using the matrix Mittag-Leffler functions ⋮ Numerical solution of fractional differential equations: a survey and a software tutorial ⋮ Bounded solutions of second order of accuracy difference schemes for semilinear fractional Schrödinger equations ⋮ A time-fractional diffusion equation with space-time dependent hidden-memory variable order: analysis and approximation ⋮ A variably distributed-order time-fractional diffusion equation: analysis and approximation ⋮ A distributed‐order fractional diffusion equation with a singular density function: Analysis and approximation ⋮ An Error Estimate of a Numerical Approximation to a Hidden-Memory Variable-Order Space-Time Fractional Diffusion Equation ⋮ A numerically efficient variational algorithm to solve a fractional nonlinear elastic string equation ⋮ Wellposedness and regularity of a variable-order space-time fractional diffusion equation ⋮ Analysis and discretization of a variable-order fractional wave equation ⋮ Generalized exponential time differencing schemes for stiff fractional systems with nonsmooth source term ⋮ A Multiprecision Derivative-Free Schur--Parlett Algorithm for Computing Matrix Functions ⋮ On oscillatory and nonoscillatory behavior of solutions for a class of fractionalorder differential equations

Uses Software

• ML

Cites Work

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