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A Hybrided Method for Temporal Variable-Order Fractional Partial Differential Equations with Fractional Laplace Operator

التفاصيل البيبلوغرافية
العنوان: A Hybrided Method for Temporal Variable-Order Fractional Partial Differential Equations with Fractional Laplace Operator
المؤلفون: Chengyi Wang, Shichao Yi
المصدر: Fractal and Fractional, Vol 8, Iss 2, p 105 (2024)
بيانات النشر: MDPI AG, 2024.
سنة النشر: 2024
المجموعة: LCC:Thermodynamics
LCC:Mathematics
LCC:Analysis
مصطلحات موضوعية: time–space fractional advection–diffusion equation, variable fractional order, nonlinearity, stability, second order, Thermodynamics, QC310.15-319, Mathematics, QA1-939, Analysis, QA299.6-433
الوصف: In this paper, we present a more general approach based on a Picard integral scheme for nonlinear partial differential equations with a variable time-fractional derivative of order α(x,t)∈(1,2) and space-fractional order s∈(0,1), where v=u′(t) is introduced as the new unknown function and u is recovered using the quadrature. In order to get rid of the constraints of traditional plans considering the half-time situation, integration by parts and the regularity process are introduced on the variable v. The convergence order can reach O(τ2+h2), different from the common L1,2−α schemes with convergence rate O(τ2,3−α(x,t)) under the infinite norm. In each integer time step, the stability, solvability and convergence of this scheme are proved. Several error results and convergence rates are calculated using numerical simulations to evidence the theoretical values of the proposed method.
نوع الوثيقة: article
وصف الملف: electronic resource
اللغة: English
تدمد: 2504-3110
Relation: https://www.mdpi.com/2504-3110/8/2/105; https://doaj.org/toc/2504-3110
DOI: 10.3390/fractalfract8020105
URL الوصول: https://doaj.org/article/23cd44e8a2c74586bd687b3621e869ea
رقم الأكسشن: edsdoj.23cd44e8a2c74586bd687b3621e869ea
قاعدة البيانات: Directory of Open Access Journals
الوصف
تدمد:25043110
DOI:10.3390/fractalfract8020105