Mass-conserving tempered fractional diffusion in a bounded interval
Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. A reflecting boundary condition enforces mass conservation on a bounded interval. In this work, explicit and implicit Euler schemes for tempered fractional diffusion with discrete reflecting or absorbing bounda...
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| Veröffentlicht in: | Fractional calculus & applied analysis 2019-12, Vol.22 (6), p.1561-1595 |
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| container_title | Fractional calculus & applied analysis |
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| creator | Lischke, Anna Kelly, James F. Meerschaert, Mark M. |
| description | Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. A reflecting boundary condition enforces mass conservation on a bounded interval. In this work, explicit and implicit Euler schemes for tempered fractional diffusion with discrete reflecting or absorbing boundary conditions are constructed. Discrete reflecting boundaries are formulated such that the Euler schemes conserve mass. Conditional stability of the explicit Euler methods and unconditional stability of the implicit Euler methods are established. Analytical steady-state solutions involving the Mittag-Leffler function are derived and shown to be consistent with late-time numerical solutions. Several numerical examples are presented to demonstrate the accuracy and usefulness of the proposed numerical schemes. |
| doi_str_mv | 10.1515/fca-2019-0081 |
| format | Article |
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Several numerical examples are presented to demonstrate the accuracy and usefulness of the proposed numerical schemes.</description><subject>33E12</subject><subject>65N12</subject><subject>Abstract Harmonic Analysis</subject><subject>Analysis</subject><subject>Boundary conditions</subject><subject>Diffusion</subject><subject>discrete reflecting boundary conditions</subject><subject>finite difference methods</subject><subject>Functional Analysis</subject><subject>Integral Transforms</subject><subject>Mathematics</subject><subject>Operational Calculus</subject><subject>Primary 26A33</subject><subject>Research Paper</subject><subject>Secondary 65M06</subject><subject>Stability analysis</subject><subject>tempered fractional derivatives</subject><issn>1311-0454</issn><issn>1314-2224</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNqFkEtLAzEURoMoWGqX7gdcp-Y9CbiR4gsqbnQd0jzKlGmmJjNK_70ZR3AjmE2-xTk3Nx8AlxgtMcf8OlgDCcIKIiTxCZhhihkkhLDT74whYpydg0XOO1SOJAIpOQOrZ5MztF3MPn00cVv1fn_wybsqJGP7poumrVwTwpBLrppYmWrTDdEVool9kUx7Ac6CabNf_Nxz8HZ_97p6hOuXh6fV7RpayuseUio58TV2yhvpbZBK1NwJap1XFHuusLG1Yww5QpUVUqHabVRAXChkGLJ0Dq6muYfUvQ8-93rXDaksmDWhDBEqRC0LBSfKpi7n5IM-pGZv0lFjpMeqdKlKj1XpsarC30z8p2nLf5zfpuFYwu_wPz1CBOZi1JeTnsszcfuvR78AK_59yw</recordid><startdate>20191201</startdate><enddate>20191201</enddate><creator>Lischke, Anna</creator><creator>Kelly, James F.</creator><creator>Meerschaert, Mark M.</creator><general>Versita</general><general>De Gruyter</general><general>Walter de Gruyter GmbH</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20191201</creationdate><title>Mass-conserving tempered fractional diffusion in a bounded interval</title><author>Lischke, Anna ; 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| ispartof | Fractional calculus & applied analysis, 2019-12, Vol.22 (6), p.1561-1595 |
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| language | eng |
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| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | 33E12 65N12 Abstract Harmonic Analysis Analysis Boundary conditions Diffusion discrete reflecting boundary conditions finite difference methods Functional Analysis Integral Transforms Mathematics Operational Calculus Primary 26A33 Research Paper Secondary 65M06 Stability analysis tempered fractional derivatives |
| title | Mass-conserving tempered fractional diffusion in a bounded interval |
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