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Modern Tools to Perform Numerical Differentiation The original
direct differential quadrature (DQ) method has been known to fail
for problems with strong nonlinearity and material discontinuity as
well as for problems involving singularity, irregularity, and
multiple scales. But now researchers in applied mathematics,
computational mechanics, and engineering have developed a range of
innovative DQ-based methods to overcome these shortcomings.
Advanced Differential Quadrature Methods explores new DQ methods
and uses these methods to solve problems beyond the capabilities of
the direct DQ method. After a basic introduction to the direct DQ
method, the book presents a number of DQ methods, including complex
DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain
DQ, and localized DQ. It also provides a mathematical compendium
that summarizes Gauss elimination, the Runge-Kutta method, complex
analysis, and more. The final chapter contains three codes written
in the FORTRAN language, enabling readers to quickly acquire
hands-on experience with DQ methods. Focusing on leading-edge DQ
methods, this book helps readers understand the majority of journal
papers on the subject. In addition to gaining insight into the
dynamic changes that have recently occurred in the field, readers
will quickly master the use of DQ methods to solve complex
problems.
Modern Tools to Perform Numerical Differentiation The original
direct differential quadrature (DQ) method has been known to fail
for problems with strong nonlinearity and material discontinuity as
well as for problems involving singularity, irregularity, and
multiple scales. But now researchers in applied mathematics,
computational mechanics, and engineering have developed a range of
innovative DQ-based methods to overcome these shortcomings.
Advanced Differential Quadrature Methods explores new DQ methods
and uses these methods to solve problems beyond the capabilities of
the direct DQ method. After a basic introduction to the direct DQ
method, the book presents a number of DQ methods, including complex
DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain
DQ, and localized DQ. It also provides a mathematical compendium
that summarizes Gauss elimination, the Runge-Kutta method, complex
analysis, and more. The final chapter contains three codes written
in the FORTRAN language, enabling readers to quickly acquire
hands-on experience with DQ methods. Focusing on leading-edge DQ
methods, this book helps readers understand the majority of journal
papers on the subject. In addition to gaining insight into the
dynamic changes that have recently occurred in the field, readers
will quickly master the use of DQ methods to solve complex
problems.
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