Fourier Analysis Of Numerical Approximations Of Hyperbolic Equations
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Fourier Analysis Of Numerical Approximations Of Hyperbolic Equations
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Author : R. Vichnevetsky
language : en
Publisher: SIAM
Release Date : 1982-01-01
Fourier Analysis Of Numerical Approximations Of Hyperbolic Equations written by R. Vichnevetsky and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Technology & Engineering categories.
This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.
Numerical Analysis Of Spectral Methods
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Author : David Gottlieb
language : en
Publisher: SIAM
Release Date : 1977-01-01
Numerical Analysis Of Spectral Methods written by David Gottlieb and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Technology & Engineering categories.
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Fourier Series Transforms And Boundary Value Problems
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Author : J. Ray Hanna
language : en
Publisher: Courier Corporation
Release Date : 2008-06-11
Fourier Series Transforms And Boundary Value Problems written by J. Ray Hanna and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-11 with Mathematics categories.
This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. Unlike most treatments, it emphasizes basic concepts and techniques rather than theory. Many of the exercises include solutions, with detailed outlines that make it easy to follow the appropriate sequence of steps. 1990 edition.
Lectures On Numerical Mathematics
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Author : H. Rutishauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Numerical Mathematics written by H. Rutishauser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present book is an edition of the manuscripts to the courses "Numerical Methods I" and "Numerical Mathematics I and II" which Professor H. Rutishauser held at the E.T.H. in Zurich. The first-named course was newly conceived in the spring semester of 1970, and intended for beginners, while the two others were given repeatedly as elective courses in the sixties. For an understanding of most chapters the funda mentals of linear algebra and calculus suffice. In some places a little complex variable theory is used in addition. However, the reader can get by without any knowledge of functional analysis. The first seven chapters discuss the direct solution of systems of linear equations, the solution of nonlinear systems, least squares prob lems, interpolation by polynomials, numerical quadrature, and approxima tion by Chebyshev series and by Remez' algorithm. The remaining chapters include the treatment of ordinary and partial differential equa tions, the iterative solution of linear equations, and a discussion of eigen value problems. In addition, there is an appendix dealing with the qd algorithm and with an axiomatic treatment of computer arithmetic.
Numerical Approximation Of Exact Controls For Waves
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Author : Sylvain Ervedoza
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-17
Numerical Approximation Of Exact Controls For Waves written by Sylvain Ervedoza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-17 with Mathematics categories.
This book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is accomplished in the abstract functional setting of conservative semigroups.The main results of the work unify, to a large extent, these two approaches, which yield similaralgorithms and convergence rates. The discrete approach, however, gives not only efficient numerical approximations of the continuous controls, but also ensures some partial controllability properties of the finite-dimensional approximated dynamics. Moreover, it has the advantage of leading to iterative approximation processes that converge without a limiting threshold in the number of iterations. Such a threshold, which is hard to compute and estimate in practice, is a drawback of the methods emanating from the continuous approach. To complement this theory, the book provides convergence results for the discrete wave equation when discretized using finite differences and proves the convergence of the discrete wave equation with non-homogeneous Dirichlet conditions. The first book to explore these topics in depth, "On the Numerical Approximations of Controls for Waves" has rich applications to data assimilation problems and will be of interest to researchers who deal with wave approximations.
Computational Aeroacoustics
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Author : Christopher K. W. Tam
language : en
Publisher: Cambridge University Press
Release Date : 2012-09-28
Computational Aeroacoustics written by Christopher K. W. Tam and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-28 with Mathematics categories.
Both a textbook for graduate students with exercises and a reference with code for researchers in computational aeroacoustics (CAA).
Direct And Large Eddy Simulation Iii
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Author : Peter R. Voke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Direct And Large Eddy Simulation Iii written by Peter R. Voke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
The practical importance of turbulence led the U.K. Royal Academy of Engineering to launch an Initiative on Turbulence, the most important outcome of which was the definition and agreement of the 1999 Newton Institute Research Programme on Turbulence. The main aim of the- month programme, held at the institute in Cambridge, was to bring together the mathematics and engineering communities involved in the turbulence area to address the many problems and to map out future strategy. As a part of the Research Programme, a Symposium on Direct and Large-Eddy Simulation was jointly organised with ERCOFfAC through their Large-Eddy Simulation Interest Group and took place in May 1999. Two previous ERCOFf AC Workshops had already taken place on these closely related varieties of turbulence simulation, at The University of Surrey in 1994 and at Universite Joseph Fourier, Grenoble in 1996. The Symposium at Cambridge was therefore the third in the ERCOFTAC series, enhanced by the presence of leading figures in the field from Europe and the USA who were resident at INI for that period of the Research Programme. Professors M. Germano, A. Leonard, J. Jimenez, R. Kerr and S. Sarkar gave the invited lectures, text versions of which will be found in this volume. As occurred at the previous two ERCOFT AC workshops, there were almost one hundred participants mostly from Europe but including some from Japan and the USA, including on this occasion resident scientists of the INI Research Programme.
Introduction To Computation And Modeling For Differential Equations
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Author : Lennart Edsberg
language : en
Publisher: John Wiley & Sons
Release Date : 2015-10-26
Introduction To Computation And Modeling For Differential Equations written by Lennart Edsberg and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-26 with Mathematics categories.
Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.
High Performance Computing For Computational Science Vecpar 2008
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Author : José M. Laginha M. Palma
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-18
High Performance Computing For Computational Science Vecpar 2008 written by José M. Laginha M. Palma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on High Performance Computing for Computational Science, VECPAR 2008, held in Toulouse, France, in June 2008. The 51 revised full papers presented together with the abstract of a surveying and look-ahead talk were carefully reviewed and selected from 73 submissions. The papers are organized in topical sections on parallel and distributed computing, cluster and grid computing, problem solving environment and data centric, numerical methods, linear algebra, computing in geosciences and biosciences, imaging and graphics, computing for aerospace and engineering, and high-performance data management in grid environments.
The Shallow Water Wave Equations Formulation Analysis And Application
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Author : Ingemar Kinnmark
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Shallow Water Wave Equations Formulation Analysis And Application written by Ingemar Kinnmark and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.