Advanced Differential Quadrature Methods
Advanced Differential Quadrature Methods by Zhi Zong, published by CRC Press LLC on June 14, 2017, is a comprehensive resource that delves into innovative numerical differentiation techniques. This edition spans 362 pages and is presented in English. The book addresses the limitations of the original direct differential quadrature (DQ) method, particularly in handling problems characterized by strong nonlinearity, material discontinuity, and singularities.
Readers will find a detailed exploration of various advanced DQ methods, including complex DQ, triangular DQ, and multi-scale DQ, among others. The text also includes a mathematical compendium summarizing essential techniques such as Gauss elimination and the Runge-Kutta method. Additionally, the final chapter features three FORTRAN codes, allowing readers to gain practical experience with these advanced methods. This book serves as a valuable guide for those in applied mathematics, computational mechanics, and engineering, facilitating a deeper understanding of contemporary DQ techniques and their applications in solving complex problems.
Official synopsis Publisher
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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