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Boundary conditions for fractional diffusion
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- Baeumer, B. (author)
- University of Otago
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- Kovacs, Mihaly, 1977 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology
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- Meerschaert, M. M. (author)
- Michigan State University
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- (creator_code:org_t)
- Elsevier BV, 2018
- 2018
- English.
- In: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 336, s. 408-424
- Journal article (peer-reviewed)
Abstract
Subject headings
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- This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivitypreserving.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Maskinteknik -- Teknisk mekanik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Mechanical Engineering -- Applied Mechanics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Fractional calculus
- Boundary value problem
- Numerical solution
- Well-posed
- partial-differential-equations
- advection-dispersion equation
- continuous-time finance
- anomalous diffusion
- numerical-solution
- vector
- calculus
- order
- approximations
- transport
- dynamics
- Mathematics
- Well-posed
Publication and Content Type
- ref (subject category)
- art (subject category)
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