Titlebook: Implementing Spectral Methods for Partial Differential Equations; Algorithms for Scien David A. Kopriva Book 2009 Springer Science+Business

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Implementing Spectral Methods for Partial Differential Equations978-90-481-2261-5Series ISSN 1434-8322 Series E-ISSN 2198-2589

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David A. KoprivaFirst book to cover multidomain spectral methods for the numerical solution of time-dependent 1D and 2D partial differential equations.Presented without too much abstract mathematics and minutae.Conta

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Scientific Computationhttp://image.papertrans.cn/i/image/462650.jpg

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https://doi.org/10.1007/978-90-481-2261-5Approximation of Derivatives; FFT Algorithm; Implementation of Spectral Methods; Multidomain Spectral M

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Algorithms for Periodic Functions, the transforms are sped up by about a factor of two by exploiting symmetries in the data and the coefficients. The chapter ends with how to approximate the derivatives of periodic functions, thus presenting the fundamental algorithms that are needed to solve partial differential equations with periodic boundary conditions.

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Survey of Spectral ApproximationsThe methods developed are the Fourier collocation and Galerkin methods, polynomial collocation and Galerkin methods, and nodal continuous and discontinuous Galerkin methods. At the end of the chapter, after it is clear what the methods are, how they are derived, and how they are implemented, a discussion is presented on how to choose between them.

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1434-8322 ose algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at the end of each chapter encourage the reader to experiment with the algorithms..978-90-481-8484-2978-90-481-2261-5Series ISSN 1434-8322 Series E-ISSN 2198-2589