大葉大學圖書館 |

Numerical integration of space fractional partial differential equations.Vol 1,Introduction to algorithms and computer coding in R /

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:	Introduction to algorithms and computer coding in R
作者:	Salehi, Younes,
其他作者:	Schiesser, W. E.,
面頁冊數:	1 PDF (xii, 189 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)
標題:	R (Computer program language)
ISBN:	9781681732084
書目註:	Includes bibliographical references and index.
內容註:	1. Introduction to fractional partial differential equations -- 1.1 Introduction -- 1.2 Computer routines, example 1 -- 1.2.1 Main program -- 1.2.2 Subordinate ODE/MOL routine -- 1.2.3 Model output -- 1.3 Computer routines, example 2 -- 1.3.1 Main program -- 1.3.2 Subordinate ODE/MOL routine -- 1.3.3 Model output -- 1.3.4 Summary and conclusions -- References --
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. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.
電子資源:	http://ieeexplore.ieee.org/servlet/opac?bknumber=8168884

Numerical integration of space fractional partial differential equations.Vol 1,Introduction to algorithms and computer coding in R /
Salehi, Younes,

Numerical integration of space fractional partial differential equations.Vol 1,Introduction to algorithms and computer coding in R /Introduction to algorithms and computer coding in RYounes Salehi, William E. Schiesser. - 1 PDF (xii, 189 pages) :illustrations. - Synthesis lectures on mathematics and statistics,# 191938-1751 ;. - Synthesis digital library of engineering and computer science..

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

Includes bibliographical references and index.

1. Introduction to fractional partial differential equations -- 1.1 Introduction -- 1.2 Computer routines, example 1 -- 1.2.1 Main program -- 1.2.2 Subordinate ODE/MOL routine -- 1.2.3 Model output -- 1.3 Computer routines, example 2 -- 1.3.1 Main program -- 1.3.2 Subordinate ODE/MOL routine -- 1.3.3 Model output -- 1.3.4 Summary and conclusions -- References --

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. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.

Mode of access: World Wide Web.

ISBN: 9781681732084

Standard No.: 10.2200/S00806ED1V01Y201709MAS019doiSubjects--Topical Terms:

689637
Fractional differential equations.
Subjects--Index Terms:

space fractional partial differential equations (SFPDEs)Index Terms--Genre/Form:

336502
Electronic books.

LC Class. No.: QA372 / .S266 2018

Dewey Class. No.: 515.353

Numerical integration of space fractional partial differential equations.Vol 1,Introduction to algorithms and computer coding in R /
LDR:05977nmm 2200601 i 4500 001 509159
003 IEEE
005 20171205115638.0
006 m eo d
007 cr cn |||m|||a
008 210514s2018 caua foab 001 0 eng d
020 $a 9781681732084 $q ebook
020 $z 9781681732077 $q print
024 7 $a 10.2200/S00806ED1V01Y201709MAS019 $2 doi
035 $a (CaBNVSL)swl00407996
035 $a (OCoLC)1013974756
035 $a 8168884
040 $a CaBNVSL $b eng $e rda $c CaBNVSL $d CaBNVSL
050 4 $a QA372 $b .S266 2018
082 0 4 $a 515.353 $2 23
100 1 $a Salehi, Younes, $e author. $3 729037
245 1 0 $a Numerical integration of space fractional partial differential equations. $n Vol 1, $p Introduction to algorithms and computer coding in R / $c Younes Salehi, William E. Schiesser.
246 3 0 $a Introduction to algorithms and computer coding in R
264 1 $a [San Rafael, California] : $b Morgan & Claypool, $c 2018.
300 $a 1 PDF (xii, 189 pages) : $b illustrations.
336 $a text $2 rdacontent
337 $a electronic $2 isbdmedia
338 $a online resource $2 rdacarrier
490 1 $a Synthesis lectures on mathematics and statistics, $x 1938-1751 ; $v # 19
500 $a Part of: Synthesis digital library of engineering and computer science.
504 $a Includes bibliographical references and index.
505 0 $a 1. Introduction to fractional partial differential equations -- 1.1 Introduction -- 1.2 Computer routines, example 1 -- 1.2.1 Main program -- 1.2.2 Subordinate ODE/MOL routine -- 1.2.3 Model output -- 1.3 Computer routines, example 2 -- 1.3.1 Main program -- 1.3.2 Subordinate ODE/MOL routine -- 1.3.3 Model output -- 1.3.4 Summary and conclusions -- References --
505 8 $a 2. Variation in the order of the fractional derivatives -- 2.1 Introduction -- 2.2 Computer routines, example 1 -- 2.2.1 Main program -- 2.2.2 Subordinate ODE/MOL routine -- 2.2.3 Model output -- 2.3 Computer routines, example 2 -- 2.3.1 Main program -- 2.3.2 Subordinate ODE/MOL routine -- 2.3.3 Model output -- 2.4 Summary and discussion --
505 8 $a 3. Dirichlet, Neumann, Robin BCs -- 3.1 Introduction -- 3.2 Example 1, Dirichlet BCs -- 3.2.1 Main program -- 3.2.2 Subordinate ODE/MOL routine -- 3.2.3 Model output -- 3.3 Example 2, Dirichlet BCs -- 3.3.1 Main program -- 3.3.2 Subordinate ODE/MOL routine -- 3.3.3 Model output -- 3.4 Example 2, Neumann BCs -- 3.4.1 Main program -- 3.4.2 Subordinate ODE/MOL routine -- 3.4.3 Model output -- 3.5 Example 2, Robin BCs -- 3.5.1 Main program -- 3.5.2 Subordinate ODE/MOL routine -- 3.5.3 Model output -- 3.6 Summary and conclusions --
505 8 $a 4. Convection SFPDEs -- 4.1 Introduction -- 4.2 Integer/fractional convection model -- 4.2.1 Main program -- 4.2.2 Subordinate ODE/MOL routine -- 4.2.3 SFPDE output -- 4.3 Summary and conclusions --
505 8 $a 5. Nonlinear SFPDEs -- 5.1 Introduction -- 5.1.1 Example 1 -- 5.1.2 Main program -- 5.1.3 Subordinate ODE/MOL routine -- 5.1.4 Model output -- 5.2 Example 2 -- 5.2.1 Main program -- 5.2.2 Subordinate ODE/MOL routine -- 5.2.3 Model output -- 5.3 Summary and conclusions --
505 8 $a A. Analytical Caputo differentiation of selected functions -- B. Derivation of a SFPDE analytical solution -- Introduction -- SFPDE equations -- Main program -- ODE/MOL routine -- Numerical output -- Summary and conclusions -- 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. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.
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 5, 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
650 0 $a R (Computer program language) $3 465792
653 $a space fractional partial differential equations (SFPDEs)
653 $a initial value (temporal) conditions
653 $a boundary value (spatial) conditions
653 $a nonlinear SFPDEs
653 $a numerical algorithms for SFPDEs
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 9781681732077
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=8168884