Numerical integration of space fractional partial differential equations.
By: Salehi, Younes [author.].
Contributor(s): Schiesser, W. E [author.].
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mathematics and statistics: # 19.Publisher: [San Rafael, California] : Morgan & Claypool, 2018.Description: 1 PDF (xii, 189 pages) : illustrations.Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681732084.Other title: Introduction to algorithms and computer coding in R.Subject(s): Fractional differential equations | Differential equations, Partial | Spatial analysis (Statistics) | R (Computer program language) | space fractional partial differential equations (SFPDEs) | initial value (temporal) conditions | boundary value (spatial) conditions | nonlinear SFPDEs | numerical algorithms for SFPDEs | fractional calculusGenre/Form: Electronic books.DDC classification: 515.353 Online resources: Abstract with links to resource Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE848 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
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 --
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 --
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 --
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 --
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 --
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.
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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.
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