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Computational methods for delay parabolic and time‐fractional partial differential equations
Author(s) -
Rihan Fathalla A.
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20504
Subject(s) - mathematics , parabolic partial differential equation , partial differential equation , stability (learning theory) , numerical partial differential equations , order (exchange) , partial derivative , first order partial differential equation , delay differential equation , mathematical analysis , scheme (mathematics) , differential equation , computer science , finance , machine learning , economics
This article is concerned with ϑ ‐methods for delay parabolic partial differential equations. The methodology is extended to time‐fractional‐order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay‐independent asymptotic stability and the solution continuously depends on the time‐fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010