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Numerical Integration
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Book Synopsis Methods of Numerical Integration by : Philip J. Davis
Download or read book Methods of Numerical Integration written by Philip J. Davis and published by Academic Press. This book was released on 2014-05-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.
Book Synopsis Geometric Numerical Integration by : Ernst Hairer
Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Book Synopsis A Concise Introduction to Geometric Numerical Integration by : Sergio Blanes
Download or read book A Concise Introduction to Geometric Numerical Integration written by Sergio Blanes and published by CRC Press. This book was released on 2017-11-22 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
Book Synopsis Numerical Integration by : Philip J. Davis
Download or read book Numerical Integration written by Philip J. Davis and published by . This book was released on 1960 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods of Numerical Integration by : Philip J. Davis
Download or read book Methods of Numerical Integration written by Philip J. Davis and published by Courier Corporation. This book was released on 2007-01-01 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful to programmers and stimulating for theoreticians, this text offers a balanced presentation accessible to those with a background in calculus. Topics include approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Includes five helpful appendixes. 1984 edition.
Book Synopsis Numerical Integration of Stochastic Differential Equations by : G.N. Milstein
Download or read book Numerical Integration of Stochastic Differential Equations written by G.N. Milstein and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.
Book Synopsis Practical Numerical Integration by : Gwynne Evans
Download or read book Practical Numerical Integration written by Gwynne Evans and published by . This book was released on 1993-08-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature. A full set of test examples is given and implemented for each method discussed, demonstrating its practical limitations.
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 Numerical Methods that Work by : Forman S. Acton
Download or read book Numerical Methods that Work written by Forman S. Acton and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A First Course in Numerical Methods by : Uri M. Ascher
Download or read book A First Course in Numerical Methods written by Uri M. Ascher and published by SIAM. This book was released on 2011-07-14 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers students a practical knowledge of modern techniques in scientific computing.
Book Synopsis Numerical Methods for Scientists and Engineers by : H.M. Antia
Download or read book Numerical Methods for Scientists and Engineers written by H.M. Antia and published by Springer Science & Business Media. This book was released on 2002-05-01 with total page 1962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems.
Book Synopsis Python Programming and Numerical Methods by : Qingkai Kong
Download or read book Python Programming and Numerical Methods written by Qingkai Kong and published by Academic Press. This book was released on 2020-11-27 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice Summaries at the end of each chapter allow for quick access to important information Includes code in Jupyter notebook format that can be directly run online
Book Synopsis A Concise Introduction to Geometric Numerical Integration by : Sergio Blanes
Download or read book A Concise Introduction to Geometric Numerical Integration written by Sergio Blanes and published by CRC Press. This book was released on 2017-11-22 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
Book Synopsis Ostrowski Type Inequalities and Applications in Numerical Integration by : Sever S. Dragomir
Download or read book Ostrowski Type Inequalities and Applications in Numerical Integration written by Sever S. Dragomir and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was noted in the preface of the book "Inequalities Involving Functions and Their Integrals and Derivatives", Kluwer Academic Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink; since the writing of the classical book by Hardy, Littlewood and Polya (1934), the subject of differential and integral inequalities has grown by about 800%. Ten years on, we can confidently assert that this growth will increase even more significantly. Twenty pages of Chapter XV in the above mentioned book are devoted to integral inequalities involving functions with bounded derivatives, or, Ostrowski type inequalities. This is now itself a special domain of the Theory of Inequalities with many powerful results and a large number of applications in Numerical Integration, Probability Theory and Statistics, Information Theory and Integral Operator Theory. The main aim of the present book, jointly written by the members of the Vic toria University node of RGMIA (Research Group in Mathematical Inequali ties and Applications, http: I /rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected number of results on Ostrowski type inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadrature for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given.
Book Synopsis Numerical Methods for Scientists and Engineers by : Zekeriya Altaç
Download or read book Numerical Methods for Scientists and Engineers written by Zekeriya Altaç and published by CRC Press. This book was released on 2024-10-15 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Scientists and Engineers: With Pseudocodes is designed as a primary textbook for a one-semester course on Numerical Methods for sophomore or junior-level students. It covers the fundamental numerical methods required for scientists and engineers, as well as some advanced topics which are left to the discretion of instructors. The objective of the text is to provide readers with a strong theoretical background on numerical methods encountered in science and engineering, and to explain how to apply these methods to practical, real-world problems. Readers will also learn how to convert numerical algorithms into running computer codes. Features: Numerous pedagogic features including exercises, “pros and cons” boxes for each method discussed, and rigorous highlighting of key topics and ideas Suitable as a primary text for undergraduate courses in numerical methods, but also as a reference to working engineers A Pseudocode approach that makes the book accessible to those with different (or no) coding backgrounds, which does not tie instructors to one particular language over another A dedicated website featuring additional code examples, quizzes, exercises, discussions, and more: https://github.com/zaltac/NumMethodsWPseudoCodes A complete Solution Manual and PowerPoint Presentations are available (free of charge) to instructors at www.routledge.com/9781032754741
Book Synopsis Numerical Methods for Engineers, Second Edition by : D. Vaughan Griffiths
Download or read book Numerical Methods for Engineers, Second Edition written by D. Vaughan Griffiths and published by CRC Press. This book was released on 2006-06-22 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although pseudocodes, Mathematica®, and MATLAB® illustrate how algorithms work, designers of engineering systems write the vast majority of large computer programs in the Fortran language. Using Fortran 95 to solve a range of practical engineering problems, Numerical Methods for Engineers, Second Edition provides an introduction to numerical methods, incorporating theory with concrete computing exercises and programmed examples of the techniques presented. Covering a wide range of numerical applications that have immediate relevancy for engineers, the book describes forty-nine programs in Fortran 95. Many of the programs discussed use a sub-program library called nm_lib that holds twenty-three subroutines and functions. In addition, there is a precision module that controls the precision of calculations. Well-respected in their field, the authors discuss a variety of numerical topics related to engineering. Some of the chapter features include... The numerical solution of sets of linear algebraic equations Roots of single nonlinear equations and sets of nonlinear equations Numerical quadrature, or numerical evaluation of integrals An introduction to the solution of partial differential equations using finite difference and finite element approaches Describing concise programs that are constructed using sub-programs wherever possible, this book presents many different contexts of numerical analysis, forming an excellent introduction to more comprehensive subroutine libraries such as the numerical algorithm group (NAG).
Book Synopsis A Critical Analysis of Various Numerical Integration Methods for Computing the Flow of a Gas in Chemical Nonequilibrium by : Harvard Lomax
Download or read book A Critical Analysis of Various Numerical Integration Methods for Computing the Flow of a Gas in Chemical Nonequilibrium written by Harvard Lomax and published by . This book was released on 1967 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
