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Numerical integration of space fractional partial differential equations.Vol 2,Applications from classical integer PDEs /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	515.353
書名/作者:	Numerical integration of space fractional partial differential equations./ Younes Salehi, William E. Schiesser.
其他題名:	Applications from classical integer PDEs
作者:	Salehi, Younes,
其他作者:	Schiesser, W. E.,
出版者:	[San Rafael, California] : : Morgan & Claypool,, 2018.
面頁冊數:	1 PDF (xii, 183-375 pages) : : illustrations.
附註:	Part of: Synthesis digital library of engineering and computer science.
標題:	Fractional differential equations.
標題:	Differential equations, Partial.
標題:	Spatial analysis (Statistics)
ISBN:	9781681732107
書目註:	Includes bibliographical references and index.
內容註:	6. Simultaneous SFPDEs -- 6.1 Introduction -- 6.2 Simultaneous SFPDEs -- 6.2.1 Main program -- 6.2.2 ODE/MOL routine -- 6.2.3 SFPDEs output -- 6.2.4 Variation of the parameters -- 6.3 Summary and conclusions --
摘要、提要註:	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: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. 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: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher-Kolmogorov SFPDE Burgers SFPDE Fokker-Planck SFPDE Burgers-Huxley SFPDE Fitzhugh-Nagumo SFPDE 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 [alpha] with 1 [less than or equal to] [alpha] [less than or equal to] 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. 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. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).
電子資源:	http://ieeexplore.ieee.org/servlet/opac?bknumber=8198764

Numerical integration of space fractional partial differential equations.Vol 2,Applications from classical integer PDEs /
Salehi, Younes,

Numerical integration of space fractional partial differential equations.Vol 2,Applications from classical integer PDEs /Applications from classical integer PDEsYounes Salehi, William E. Schiesser. - [San Rafael, California] :Morgan & Claypool,2018. - 1 PDF (xii, 183-375 pages) :illustrations. - Synthesis lectures on mathematics and statistics,# 201938-1751 ;. - Synthesis digital library of engineering and computer science..

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references and index.

6. Simultaneous SFPDEs -- 6.1 Introduction -- 6.2 Simultaneous SFPDEs -- 6.2.1 Main program -- 6.2.2 ODE/MOL routine -- 6.2.3 SFPDEs output -- 6.2.4 Variation of the parameters -- 6.3 Summary and conclusions --

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Compendex

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: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. 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: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher-Kolmogorov SFPDE Burgers SFPDE Fokker-Planck SFPDE Burgers-Huxley SFPDE Fitzhugh-Nagumo SFPDE 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 [alpha] with 1 [less than or equal to] [alpha] [less than or equal to] 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. 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. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).

Mode of access: World Wide Web.

ISBN: 9781681732107

Standard No.: 10.2200/S00808ED1V02Y201710MAS020doiSubjects--Topical Terms:

689637
Fractional differential equations.
Subjects--Index Terms:

partial differential equationsIndex Terms--Genre/Form:

336502
Electronic books.

LC Class. No.: QA372 / .S2662 2018

Dewey Class. No.: 515.353

Numerical integration of space fractional partial differential equations.Vol 2,Applications from classical integer PDEs /
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264 1 $a [San Rafael, California] : $b Morgan & Claypool, $c 2018.
300 $a 1 PDF (xii, 183-375 pages) : $b illustrations.
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337 $a electronic $2 isbdmedia
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490 1 $a Synthesis lectures on mathematics and statistics, $x 1938-1751 ; $v # 20
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504 $a Includes bibliographical references and index.
505 0 $a 6. Simultaneous SFPDEs -- 6.1 Introduction -- 6.2 Simultaneous SFPDEs -- 6.2.1 Main program -- 6.2.2 ODE/MOL routine -- 6.2.3 SFPDEs output -- 6.2.4 Variation of the parameters -- 6.3 Summary and conclusions --
505 8 $a 7. Two sided SFPDEs -- 7.1 Introduction -- 7.2 Two-sided convective SFPDE, Caputo derivatives -- 7.2.1 Main program -- 7.2.2 ODE/MOL routine -- 7.2.3 SFPDE output -- 7.3 Two-sided convective SFPDE, Riemann-Liouville derivatives -- 7.3.1 Main program -- 7.3.2 ODE/MOL routine -- 7.3.3 SFPDE output -- 7.4 Summary and conclusions --
505 8 $a 8. Integer to fractional extensions -- 8.1 Introduction -- 8.2 Fractional diffusion equation -- 8.2.1 Main program, Dirchlet BCs -- 8.2.2 ODE/MOL routine -- 8.2.3 Model output -- 8.2.4 Main program, Neumann BCs -- 8.2.5 ODE/MOL routine -- 8.2.6 Model output -- 8.2.7 Main program, Robin BCs -- 8.2.8 ODE/MOL routine -- 8.2.9 Model output -- 8.3 Fractional Burgers equation -- 8.3.1 Main program, Dirchlet BCs -- 8.3.2 ODE/MOL routine -- 8.3.3 Model output -- 8.4 Fractional Fokker-Planck equation -- 8.4.1 Main program -- 8.4.2 ODE/MOL routine -- 8.4.3 Model output -- 8.5 Fractional Burgers-Huxley equation -- 8.5.1 Main program -- 8.5.2 ODE/MOL routine -- 8.5.3 Model output -- 8.6 Fractional Fitzhugh-Nagumo equation -- 8.6.1 Main program -- 8.6.2 ODE/MOL routine -- 8.6.3 Model output -- 8.7 Summary and conclusions --
505 8 $a Authors' biographies -- Index.
506 $a Abstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0 $a Compendex
510 0 $a INSPEC
510 0 $a Google scholar
510 0 $a Google book search
520 3 $a 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: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. 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: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher-Kolmogorov SFPDE Burgers SFPDE Fokker-Planck SFPDE Burgers-Huxley SFPDE Fitzhugh-Nagumo SFPDE 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 [alpha] with 1 [less than or equal to] [alpha] [less than or equal to] 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. 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. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).
530 $a Also available in print.
538 $a Mode of access: World Wide Web.
538 $a System requirements: Adobe Acrobat Reader.
588 $a Title from PDF title page (viewed on December 12, 2017).
650 0 $a Fractional differential equations. $3 689637
650 0 $a Differential equations, Partial. $3 389324
650 0 $a Spatial analysis (Statistics) $3 435535
653 $a partial differential equations
653 $a value variables
653 $a space fractional partial differential equations
653 $a fractional calculus
655 0 $a Electronic books. $2 local $3 336502
700 1 $a Schiesser, W. E., $e author. $3 729012
776 0 8 $i Print version: $z 9781681732091
830 0 $a Synthesis digital library of engineering and computer science. $3 461208
830 0 $a Synthesis lectures on mathematics and statistics ; $v # 22. $x 1938-1751 $3 729013
856 4 2 $3 Abstract with links to resource $u http://ieeexplore.ieee.org/servlet/opac?bknumber=8198764