Advanced Differential Quadrature Methods

ISBN-13: 9781138117907 / Angielski / Miękka / 2017 / 362 str.

Zhi Zong;Yingyan Zhang

Opis

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.

Spis treści

Approximation and Differential Quadrature. Complex Differential Quadrature Method. Triangular Differential Quadrature Method. Multiple Scale Differential Quadrature Method. Variable Order Differential Quadrature Method. Multi-Domain Differential Quadrature Method. Localized Differential Quadrature Method. Codes. Mathematical Compendium. Codes. References. Index.

O autorze

Yingyan Zhang, Zhi Zong