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Numerical Integration of Space Fractional Partial Differential Equations - Vol 1 - Introduction to Algorithms and Computer Coding in R (Paperback)
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Numerical Integration of Space Fractional Partial Differential Equations - Vol 1 - Introduction to Algorithms and Computer Coding in R (Paperback)
Series: Synthesis Lectures on Mathematics & Statistics
Expected to ship within 10 - 15 working days
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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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