Author: R. Vichnevetsky Publisher: SIAM ISBN: 9781611970876 Category : Technology & Engineering Languages : en Pages : 152
Book Description
There has been a growing interest in the use of Fourier analysis to examine questions of accuracy and stability of numerical methods for solving partial differential equations. This kind of analysis can produce particularly attractive and useful results for hyperbolic equations. This book provides useful reference material for those concerned with computational fluid dynamics: for physicists and engineers who work with computers in the analysis of problems in such diverse fields as hydraulics, gas dynamics, plasma physics, numerical weather prediction, and transport processes in engineering, and who need to understand the implications of the approximations they use; and for applied mathematicians concerned with the more theoretical aspects of these computations.
Author: David Gottlieb Publisher: SIAM ISBN: 0898710235 Category : Technology & Engineering Languages : en Pages : 167
Book Description
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.
Author: H. Rutishauser Publisher: Springer Science & Business Media ISBN: 1461234689 Category : Mathematics Languages : en Pages : 559
Book Description
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.
Author: J. Ray Hanna Publisher: Courier Corporation ISBN: 0486466736 Category : Mathematics Languages : en Pages : 370
Book Description
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.
Author: Randall J. LeVeque Publisher: SIAM ISBN: 9780898717839 Category : Mathematics Languages : en Pages : 356
Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Author: Sylvain Ervedoza Publisher: Springer Science & Business Media ISBN: 1461458080 Category : Mathematics Languages : en Pages : 140
Book Description
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.
Author: Bertil Gustafsson Publisher: John Wiley & Sons ISBN: 1118548523 Category : Mathematics Languages : en Pages : 464
Book Description
Praise for the First Edition ". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods. The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and their application to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations.
Author: Christopher K. W. Tam Publisher: Cambridge University Press ISBN: 1139576569 Category : Technology & Engineering Languages : en Pages : 497
Book Description
Computational aeroacoustics (CAA) is a relatively new research area. CAA algorithms have developed rapidly and the methods have been applied in many areas of aeroacoustics. The objective of CAA is not simply to develop computational methods but also to use these methods to solve practical aeroacoustics problems and to perform numerical simulation of aeroacoustic phenomena. By analysing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. This is both a textbook for graduate students and a reference for researchers in CAA and as such is self-contained. No prior knowledge of numerical methods for solving partial differential equations (PDEs) is needed, however, a general understanding of partial differential equations and basic numerical analysis is assumed. Exercises are included and are designed to be an integral part of the chapter content. In addition, sample computer programs are included to illustrate the implementation of the numerical algorithms.
Author: Peter R. Voke Publisher: Springer Science & Business Media ISBN: 9401592853 Category : Science Languages : en Pages : 452
Book Description
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.
Author: Lennart Edsberg Publisher: John Wiley & Sons ISBN: 1119018463 Category : Mathematics Languages : en Pages : 285
Book Description
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.
Author: R. Vichnevetsky
Author: David Gottlieb
Author: H. Rutishauser
Author: J. Ray Hanna
Author: Randall J. LeVeque
Author: Sylvain Ervedoza
Author: Bertil Gustafsson
Author: Christopher K. W. Tam
Author: Peter R. Voke
Author: Lennart Edsberg