Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on R 2 and the solution on the square is regarded as a localization. For the numerical approxi...
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| Veröffentlicht in: | Applications of mathematics (Prague) 2017-02, Vol.62 (1), p.15-36 |
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| creator | Szekeres, Béla J. Izsák, Ferenc |
| description | Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on R
2
and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the complicated approximations of fractional order derivatives. The spatial convergence of this method is proved and demonstrated by some numerical experiments. |
| doi_str_mv | 10.21136/AM.2017.0385-15 |
| format | Article |
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and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the complicated approximations of fractional order derivatives. The spatial convergence of this method is proved and demonstrated by some numerical experiments.</description><identifier>ISSN: 0862-7940</identifier><identifier>EISSN: 1572-9109</identifier><identifier>DOI: 10.21136/AM.2017.0385-15</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Applications of Mathematics ; Approximation ; Boundary conditions ; Calculus ; Classical and Continuum Physics ; Convergence ; Derivatives ; Diffusion ; Dirichlet problem ; Error analysis ; Experiments ; Finite difference method ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Measurement techniques ; Optimization ; Scholarships & fellowships ; Studies ; Theoretical</subject><ispartof>Applications of mathematics (Prague), 2017-02, Vol.62 (1), p.15-36</ispartof><rights>Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017</rights><rights>Applications of Mathematics is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p258t-9c1f3962626f4b42eedeaf6d1331621a459a4ffce0ea06e38f2f686be2ccc1473</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.21136/AM.2017.0385-15$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.21136/AM.2017.0385-15$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Szekeres, Béla J.</creatorcontrib><creatorcontrib>Izsák, Ferenc</creatorcontrib><title>Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems</title><title>Applications of mathematics (Prague)</title><addtitle>Appl Math</addtitle><description>Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on R
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and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the complicated approximations of fractional order derivatives. 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| source | Springer Online Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Analysis Applications of Mathematics Approximation Boundary conditions Calculus Classical and Continuum Physics Convergence Derivatives Diffusion Dirichlet problem Error analysis Experiments Finite difference method Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Measurement techniques Optimization Scholarships & fellowships Studies Theoretical |
| title | Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems |
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