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Theory And Applications Of Gaussian Quadrature Methods
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Book Synopsis Theory and Applications of Gaussian Quadrature Methods by : Narayan Kovvali
Download or read book Theory and Applications of Gaussian Quadrature Methods written by Narayan Kovvali and published by Morgan & Claypool Publishers. This book was released on 2011 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions, and examine the analytical framework of Gaussian quadrature. We discuss Gaussian quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of Gaussian quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided.
Book Synopsis Theory and Applications of Gaussian Quadrature Methods by : Narayan Kovvali
Download or read book Theory and Applications of Gaussian Quadrature Methods written by Narayan Kovvali and published by Springer Nature. This book was released on 2022-05-31 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions and examine the analytical framework of Gaussian quadrature. We discuss Gaussian quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of Gaussian quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided. Table of Contents: Introduction / Approximating with Polynomials and Related Functions / Gaussian Quadrature / Applications / Links to Mathematical Software
Download or read book Quadrature Theory written by Helmut Brass and published by American Mathematical Soc.. This book was released on 2011-10-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.
Book Synopsis Differential Quadrature and Differential Quadrature Based Element Methods by : Xinwei Wang
Download or read book Differential Quadrature and Differential Quadrature Based Element Methods written by Xinwei Wang and published by Butterworth-Heinemann. This book was released on 2015-03-24 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications is a comprehensive guide to these methods and their various applications in recent years. Due to the attractive features of rapid convergence, high accuracy, and computational efficiency, the differential quadrature method and its based element methods are increasingly being used to study problems in the area of structural mechanics, such as static, buckling and vibration problems of composite structures and functional material structures. This book covers new developments and their applications in detail, with accompanying FORTRAN and MATLAB programs to help you overcome difficult programming challenges. It summarises the variety of different quadrature formulations that can be found by varying the degree of polynomials, the treatment of boundary conditions and employing regular or irregular grid points, to help you choose the correct method for solving practical problems. Offers a clear explanation of both the theory and many applications of DQM to structural analyses Discusses and illustrates reliable ways to apply multiple boundary conditions and develop reliable grid distributions Supported by FORTRAN and MATLAB programs, including subroutines to compute grid distributions and weighting coefficients
Book Synopsis Numerical Integration by : T.O. Espelid
Download or read book Numerical Integration written by T.O. Espelid and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Develop ments, Software and Applications', held at the University of Bergen, Bergen, Norway, June 17-21,1991. The Workshop was attended by thirty-eight scientists. A total of eight NATO countries were represented. Eleven invited lectures and twenty-three contributed lectures were presented, of which twenty-five appear in full in this volume, together with three extended abstracts and one note. The main focus of the workshop was to survey recent progress in the theory of methods for the calculation of integrals and show how the theoretical results have been used in software development and in practical applications. The papers in this volume fall into four broad categories: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software. It is five years since the last workshop of this nature was held, at Dalhousie University in Halifax, Canada, in 1986. Recent theoretical developments have mostly occurred in the area of integration rule construction. For polynomial integrating rules, invariant theory and ideal theory have been used to provide lower bounds on the numbers of points for different types of multidimensional rules, and to help in structuring the nonlinear systems which must be solved to determine the points and weights for the rules. Many new optimal or near optimal rules have been found for a variety of integration regions using these techniques.
Book Synopsis An Introduction to Numerical Methods by : Abdelwahab Kharab
Download or read book An Introduction to Numerical Methods written by Abdelwahab Kharab and published by CRC Press. This book was released on 2005-07-27 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical methods are a mainstay of researchers and professionals across the many mathematics, scientific, and engineering disciplines. The importance of these methods combined with the power and availability of today's computers virtually demand that students in these fields be well versed not only in the numerical techniques, but also in the use of a modern computational software package. Updated to reflect the latest version of MATLAB, the second edition of An Introduction to Numerical Methods continues to fulfill both these needs. It introduces the theory and applications of the most commonly used techniques for solving numerical problems on a computer. It covers a wide range of useful algorithms, each presented with full details so that readers can visualize and interpret each step. Highlights of the second edition: A new chapter on numerical optimization New sections on finite elements More exercises and applied problems in each chapter MATLAB incorporated as an integral part of the text Emphasis on understanding how the methods work, a simple, direct style, and thorough coverage make this book an outstanding initiation that allows students to see almost immediate results. It will boost their confidence in their ability to master the subject and give them valuable experience in the use of MATLAB.
Book Synopsis Differential Quadrature and Its Application in Engineering by : Chang Shu
Download or read book Differential Quadrature and Its Application in Engineering written by Chang Shu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed. The book contains material on: - Linear Vector Space Analysis and the Approximation of a Function; - Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature; - Differential Quadrature Weighting Coefficient Matrices; - Solution of Differential Quadrature-resultant Equations; - The Solution of Incompressible Navier-Stokes and Helmholtz Equations; - Structural and Vibrational Analysis Applications; - Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations. Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.
Book Synopsis Theories and Applications of Plate Analysis by : Rudolph Szilard
Download or read book Theories and Applications of Plate Analysis written by Rudolph Szilard and published by John Wiley & Sons. This book was released on 2004-01-02 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book by a renowned structural engineer offers comprehensive coverage of both static and dynamic analysis of plate behavior, including classical, numerical, and engineering solutions. It contains more than 100 worked examples showing step by step how the various types of analysis are performed.
Book Synopsis Evaluation of the First and Second Moment Integrals of a Certain Probability Density Function by an Application of the Theory of Gaussian Quadrature by : J. R. Johler
Download or read book Evaluation of the First and Second Moment Integrals of a Certain Probability Density Function by an Application of the Theory of Gaussian Quadrature written by J. R. Johler and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis U.S. Government Research & Development Reports by :
Download or read book U.S. Government Research & Development Reports written by and published by . This book was released on 1969-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Gauss Quadrature Rules Involving Some Nonclassical Weight Functions by : Paul F. Byrd
Download or read book Gauss Quadrature Rules Involving Some Nonclassical Weight Functions written by Paul F. Byrd and published by . This book was released on 1970 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Least-Squares Finite Element Method by : Bo-nan Jiang
Download or read book The Least-Squares Finite Element Method written by Bo-nan Jiang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
Book Synopsis Quadrature Formulae by : Aldo Ghizzetti
Download or read book Quadrature Formulae written by Aldo Ghizzetti and published by . This book was released on 1970 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Methods in Chemistry and Physics by : Bernard Shizgal
Download or read book Spectral Methods in Chemistry and Physics written by Bernard Shizgal and published by Springer. This book was released on 2015-01-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.
Book Synopsis The Finite Element Method and Its Reliability by : Ivo Babuška
Download or read book The Finite Element Method and Its Reliability written by Ivo Babuška and published by Oxford University Press. This book was released on 2001 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.
Book Synopsis Control and Dynamic Systems V56: Digital and Numeric Techniques and Their Application in Control Systems by : C.T. Leonides
Download or read book Control and Dynamic Systems V56: Digital and Numeric Techniques and Their Application in Control Systems written by C.T. Leonides and published by Academic Press. This book was released on 2012-12-02 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and Dynamic Systems: Advances in Theory and Applications, Volume 56: Digital and Numeric Techniques and their Applications in Control Systems, Part 2 of 2 covers the significant developments in digital and numerical techniques for the analysis and design of modern complex control systems. This volume is composed of 12 chapters and starts with a description of the design techniques of linear constrained discrete-time control systems. The subsequent chapters describe the techniques dealing with robust real-time system identification, the adaptive control algorithms, and the utilization of methods from generalized interpolation and operator theory to deal with a wide range of problems in robust control. These topics are followed by reviews f the decentralized control design for interconnected uncertain systems; the computation of frequency response of descriptor systems by rational interpolation; the techniques for the synthesis of multivariable feedback control laws; and the effect of the initial condition in state estimation for discrete-time linear systems. Other chapters illustrate practical, efficient, and reliable numerical algorithms for robust multivariable control design of linear time-invariant systems, as well as a complete analysis of closed-loop transfer recovery in discrete-time systems using observer-based controllers. The last chapters provide the techniques in robust policy-making in the global economic environment and the implications of robust control techniques for continuous-time systems. This book will prove useful to process, control, systems, and design engineers.
Book Synopsis Practical Extrapolation Methods by : Avram Sidi
Download or read book Practical Extrapolation Methods written by Avram Sidi and published by Cambridge University Press. This book was released on 2003-06-05 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
