»ã±¨±êÌâ (Title)£ºThe Positive Definiteness of the Integral-Averaged L1 (IAL1) Fractional Derivative Operator and its Application in H?-norm Analysis of the IAL1 Method (»ý·Ôì½¾ùL1(IAL1)·ÖÊý½×µ¼Ëã×ÓµÄÕý¶¨ÐÔ¼°ÆäÔÚIAL1²½ÖèH?·¶Êý·ÖÎöÖеÄÀûÓÃÄÚ£©

»ã±¨ÈË (Speaker)£ºÍõÔªÃ÷ ½ÌÊÚ£¨»ª¶«Ê¦·¶´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê6ÔÂ11ÈÕ£¨ÖÜÈý£©8:30-10:30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÀƷ¡¢²ÌÃô

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»ã±¨ÌáÒª£ºA new positive definiteness result for the integral-averaged L1 (IAL1) fractional-derivative operator is established. It improves the previous positive definiteness results in the literature and plays an important role in the analysis of H?-norm error of the IAL1 method. Using this new positive definiteness result, we give an H?-norm analysis of the stability and convergence of the IAL1 method for a time-fractional diffusion problem with a Caputo time-fractional derivative of order ¦Á¡Ê(0,1) on nonuniform time meshes. The H?-norm stability holds for the general nonuniform time meshes, while the H?-norm convergence is proved for the time graded meshes and the H?-norm convergence order in time is min{3 + ¦Á,¦Ã¦Á}/2 for all ¦Á¡Ê(0, 1), where ¦Ã ¡Ý 1 is the mesh grading parameter. Two full discretization methods using finite differences and finite elements in space are considered. The theoretical results are illustrated by numerical results.