Research in Applied Mathematics

Abstract

A Finite Difference Scheme for theTime-Fractional Landau-Lifshitz-Bloch Equation

Author(s): C.Ayouch,E.H.Essoufi,and M.Tilioua

Inthispaper,westudyafinitedifferenceschemefortemporaldiscretizationofthe time-fractionalLandau-Lifshitz-Blochequation,suchasthefractionaltimederivativeoforder 𝛼istakeninthesenseofCaputo.Anexistenceresultisestablishedforthesemi-discreteproblem bySchaefer’sfixedpointtheorem.Stabilityanderroranalysisarethenprovided,showingthat thetemporalaccuracyisoforder2−𝛼.

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