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A Finite Di??erence Scheme for theTime-Fractional Landau-Lifshitz-Bloch Equation | Abstract

Research in Applied Mathematics

Abstract

A Finite Di??erence Scheme for theTime-Fractional Landau-Lifshitz-Bloch Equation

Author(s): C.Ayouch,E.H.Essou├»┬Č┬ü,and M.Tilioua

Inthispaper,westudya?nitedi??erenceschemefortemporaldiscretizationofthe time-fractionalLandau-Lifshitz-Blochequation,suchasthefractionaltimederivativeoforder ???istakeninthesenseofCaputo.Anexistenceresultisestablishedforthesemi-discreteproblem bySchaefer’s?xedpointtheorem.Stabilityanderroranalysisarethenprovided,showingthat thetemporalaccuracyisoforder2−???.

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