A Practical Guide to Pseudospectral Methods PDF Download

Author: Bengt Fornberg
Publisher: Cambridge University Press
ISBN: 9780521645645
Category : Mathematics
Languages : en
Pages : 248

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Book Description
This book explains how, when and why the pseudospectral approach works.

Author: Bengt Fornberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 231

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Author: Elizabeth Louise Mansfield
Publisher: Cambridge University Press
ISBN: 1139487043
Category : Mathematics
Languages : en
Pages : 261

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Book Description
This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.

Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486411834
Category : Mathematics
Languages : en
Pages : 690

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Book Description
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Author: George Rawitscher
Publisher: Springer
ISBN: 3319427032
Category : Science
Languages : en
Pages : 221

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Book Description
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.

Author: Sedat Biringen
Publisher: John Wiley & Sons
ISBN: 0470915153
Category : Science
Languages : en
Pages : 322

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Book Description
This new book builds on the original classic textbook entitled: An Introduction to Computational Fluid Mechanics by C. Y. Chow which was originally published in 1979. In the decades that have passed since this book was published the field of computational fluid dynamics has seen a number of changes in both the sophistication of the algorithms used but also advances in the computer hardware and software available. This new book incorporates the latest algorithms in the solution techniques and supports this by using numerous examples of applications to a broad range of industries from mechanical and aerospace disciplines to civil and the biosciences. The computer programs are developed and available in MATLAB. In addition the core text provides up-to-date solution methods for the Navier-Stokes equations, including fractional step time-advancement, and pseudo-spectral methods. The computer codes at the following website: www.wiley.com/go/biringen

Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 1611975948
Category : Mathematics
Languages : en
Pages : 375

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Book Description
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the field’s most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.

Author: Michael Halliwell
Publisher: Springer Science & Business Media
ISBN: 0306471078
Category : Technology & Engineering
Languages : en
Pages : 571

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Book Description
The origin ofthe International Acoustical Imaging Symposium series can be traced to 1967, when a meeting on acoustical holography was held in C alifornia. In those days, acoustical holography was at the leading edge of research but, as the importance of this subject waned, so the title of the series was changed from Acoustical Holography to Acoustical Imaging in 1978. The early Symposia were held at various venues in the United States. In 1980. the series became international, with the Symposium that year taking place in Cannes in France. The pattern now is to try to met alternately in the USA and in another part of the world so that active researchers everywhere can conveniently attend at a reasonably high frequency. It was a great privilege for us in Bristol in the United Kingdom to be chosen to host the 25th Symposium, which convened on 19 March 2000 and spread over four days. We were blessed not only by good weather, but also by the attendance ofnearly 100 pa rticipants who came from 17 c ountries. A large number of papers were accepted for presentation, either orally or as posters. Whether an oral presentation or a poster, all were considered to have equal merit, and no distinction is made between them in the published proceedings. There were no parallel sessions, so every participant could attend every presentation. The re sultant disciplinary cross fertilisation maintained the t radition of past Symposia.

Author: Stavros C. Farantos
Publisher: Springer
ISBN: 3319099884
Category : Science
Languages : en
Pages : 165

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Book Description
This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.

Author: Mark Ainsworth
Publisher: Springer Science & Business Media
ISBN: 3642554830
Category : Mathematics
Languages : en
Pages : 408

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Book Description
These ten detailed and authoritative survey articles on numerical methods for direct and inverse wave propagation problems are written by leading experts. Researchers and practitioners in computational wave propagation, from postgraduate level onwards, will find the breadth and depth of coverage of recent developments a valuable resource. The articles describe a wide range of topics on the application and analysis of methods for time and frequency domain PDE and boundary integral formulations of wave propagation problems. Electromagnetic, seismic and acoustic equations are considered. Recent developments in methods and analysis ranging from finite differences to hp-adaptive finite elements, including high-accuracy and fast methods are described with extensive references.