Chebyshev and Fourier Spectral Methods

Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486141926
Format: PDF, Mobi
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Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

A Theoretical Introduction to Numerical Analysis

Author: Victor S. Ryaben'kii
Publisher: CRC Press
ISBN: 1420011162
Format: PDF, Mobi
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A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

Free Surface Flow

Author: Nikolaos D. Katopodes
Publisher: Butterworth-Heinemann
ISBN: 0128154861
Format: PDF, Docs
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Free-Surface Flow: Computational Methods presents a detailed analysis of numerical schemes for shallow-water waves. It includes practical applications for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow. Closure models for turbulence, such as Reynolds-Averaged Navier-Stokes and Large Eddy Simulation are presented, coupling the aforementioned surface tracking techniques with environmental fluid dynamics. While many computer programs can solve the partial differential equations describing the dynamics of fluids, many are not capable of including free surfaces in their simulations. Provides numerical solutions of the turbulent Navier-Stokes equations in three space dimensions Includes closure models for turbulence, such as Reynolds-Averaged Navier-Stokes, and Large Eddy Simulation Practical applications are presented for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow