000 04331nam a22005295i 4500
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008 220601s2018 sz | s |||| 0|eng d
020 _a9783031024122
_9978-3-031-02412-2
024 7 _a10.1007/978-3-031-02412-2
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
072 7 _aPB
_2thema
082 0 4 _a510
_223
100 1 _aSalehi, Younes.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984342
245 1 0 _aNumerical Integration of Space Fractional Partial Differential Equations
_h[electronic resource] :
_bVol 2 - Applications from Classical Integer PDEs /
_cby Younes Salehi, William E. Schiesser.
250 _a1st ed. 2018.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
300 _aXII, 192 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Mathematics & Statistics,
_x1938-1751
505 0 _aPreface -- Simultaneous SFPDEs -- Two Sided SFPDEs -- Integer to Fractional Extensions -- Authors' Biographies -- Index.
520 _a<p>Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as:</p><div><ul></div><div><li>Vol 1: Introduction to Algorithms and Computer Coding in R</li></div> <li>Vol 2: Applications from Classical Integer PDEs.</li></div><div></ul></div><div><p>Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative.</p></div><div><p>In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are:</p></div><div><ul></div> <li>Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions <li>Fisher-Kolmogorov SFPDE</li></div><div><li>Burgers SFPDE</li></div><div><li>Fokker-Planck SFPDE</li></div><div><li>Burgers-Huxley SFPDE</li></div><div><li>Fitzhugh-Nagumo SFPDE</li></div></ul></div><div><p>These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order ���� with 1 ≤ ���� ≤ 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume.</p></div><div><p>The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume.</p></div><div><p>The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).</p></div></div>.
650 0 _aMathematics.
_911584
650 0 _aStatistics .
_931616
650 0 _aEngineering mathematics.
_93254
650 1 4 _aMathematics.
_911584
650 2 4 _aStatistics.
_914134
650 2 4 _aEngineering Mathematics.
_93254
700 1 _aSchiesser, William E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984345
710 2 _aSpringerLink (Online service)
_984348
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031002588
776 0 8 _iPrinted edition:
_z9783031012846
776 0 8 _iPrinted edition:
_z9783031035401
830 0 _aSynthesis Lectures on Mathematics & Statistics,
_x1938-1751
_984350
856 4 0 _uhttps://doi.org/10.1007/978-3-031-02412-2
912 _aZDB-2-SXSC
942 _cEBK
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