Differential Quadrature and Its Application in Engineering:
In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed imp...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
2000
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| Schlagworte: | |
| Online-Zugang: | FHI01 BTU01 Volltext |
| Zusammenfassung: | In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems |
| Beschreibung: | 1 Online-Ressource (XVI, 340 p) |
| ISBN: | 9781447104070 |
| DOI: | 10.1007/978-1-4471-0407-0 |
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| 520 | |a In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Shu, Chang |
| author_facet | Shu, Chang |
| author_role | aut |
| author_sort | Shu, Chang |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-0407-0 |
| format | Electronic eBook |
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| id | DE-604.BV045148742 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:10:02Z |
| institution | BVB |
| isbn | 9781447104070 |
| language | English |
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| oclc_num | 1050951436 |
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| owner_facet | DE-573 DE-634 |
| physical | 1 Online-Ressource (XVI, 340 p) |
| psigel | ZDB-2-ENG ZDB-2-ENG_2000/2004 ZDB-2-ENG ZDB-2-ENG_2000/2004 ZDB-2-ENG ZDB-2-ENG_Archiv |
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| publisher | Springer London |
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| spelling | Shu, Chang Verfasser aut Differential Quadrature and Its Application in Engineering by Chang Shu London Springer London 2000 1 Online-Ressource (XVI, 340 p) txt rdacontent c rdamedia cr rdacarrier In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems Engineering Appl.Mathematics/Computational Methods of Engineering Analysis Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering mathematics Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Technik (DE-588)4059205-4 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Technik (DE-588)4059205-4 s 1\p DE-604 Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 9781447111320 https://doi.org/10.1007/978-1-4471-0407-0 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shu, Chang Differential Quadrature and Its Application in Engineering Engineering Appl.Mathematics/Computational Methods of Engineering Analysis Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering mathematics Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Technik (DE-588)4059205-4 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4128130-5 (DE-588)4059205-4 |
| title | Differential Quadrature and Its Application in Engineering |
| title_auth | Differential Quadrature and Its Application in Engineering |
| title_exact_search | Differential Quadrature and Its Application in Engineering |
| title_full | Differential Quadrature and Its Application in Engineering by Chang Shu |
| title_fullStr | Differential Quadrature and Its Application in Engineering by Chang Shu |
| title_full_unstemmed | Differential Quadrature and Its Application in Engineering by Chang Shu |
| title_short | Differential Quadrature and Its Application in Engineering |
| title_sort | differential quadrature and its application in engineering |
| topic | Engineering Appl.Mathematics/Computational Methods of Engineering Analysis Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering mathematics Differentialgleichung (DE-588)4012249-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Technik (DE-588)4059205-4 gnd |
| topic_facet | Engineering Appl.Mathematics/Computational Methods of Engineering Analysis Mathematical analysis Analysis (Mathematics) Applied mathematics Engineering mathematics Differentialgleichung Numerisches Verfahren Technik |
| url | https://doi.org/10.1007/978-1-4471-0407-0 |
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