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An Introductory Guide to Computational Methods for the Solution of Physics Problems - With Emphasis on Spectral Methods (Paperback, 1st ed. 2018)
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An Introductory Guide to Computational Methods for the Solution of Physics Problems - With Emphasis on Spectral Methods (Paperback, 1st ed. 2018)
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This monograph presents fundamental aspects of modern spectral and
other computational methods, which are not generally taught in
traditional courses. It emphasizes concepts as errors, convergence,
stability, order and efficiency applied to the solution of physical
problems. The spectral methods consist in expanding the function to
be calculated into a set of appropriate basis functions (generally
orthogonal polynomials) and the respective expansion coefficients
are obtained via collocation equations. The main advantage of these
methods is that they simultaneously take into account all available
information, rather only the information available at a limited
number of mesh points. They require more complicated matrix
equations than those obtained in finite difference methods.
However, the elegance, speed, and accuracy of the spectral methods
more than compensates for any such drawbacks. During the course of
the monograph, the authors examine the usually rapid convergence of
the spectral expansions and the improved accuracy that results when
nonequispaced support points are used, in contrast to the
equispaced points used in finite difference methods. In particular,
they demonstrate the enhanced accuracy obtained in the solutionof
integral equations. The monograph includes an informative
introduction to old and new computational methods with numerous
practical examples, while at the same time pointing out the errors
that each of the available algorithms introduces into the specific
solution. It is a valuable resource for undergraduate students as
an introduction to the field and for graduate students wishing to
compare the available computational methods. In addition, the work
develops the criteria required for students to select the most
suitable method to solve the particular scientific problem that
they are confronting.
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