Positivity of discrete time-fractional operators with applications to phase-field equations

SAMIR KARAA*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمراجعة النظراء

3 اقتباسات (Scopus)

ملخص

We present general criteria ensuring the positivity of quadratic forms of convolution type generated by sequences of real numbers. A sharp result is obtained in the case of completely monotone sequences. Applications to widely used approximations of fractional integral and differential operators, including convolution quadrature and L1 formula on uniform temporal meshes, are presented and new inequalities are established. The results are found to be fundamental in the investigation of the numerical stability for time-fractional phase-field models. It is shown through a standard energy stability analysis and without the use of a fractional Grönwall inequality that several numerical schemes satisfy discrete energy dissipation laws.

اللغة الأصليةEnglish
الصفحات (من إلى)2040-2053
عدد الصفحات14
دوريةSIAM Journal on Numerical Analysis
مستوى الصوت59
رقم الإصدار4
المعرِّفات الرقمية للأشياء
حالة النشرPublished - 2021

ASJC Scopus subject areas

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بصمة

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