Author: Gwynne Evans Publisher: ISBN: Category : Mathematics Languages : en Pages : 350
Book Description
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.
Author: Philip J. Davis Publisher: Academic Press ISBN: 1483264289 Category : Mathematics Languages : en Pages : 628
Book Description
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.
Author: Ernst Hairer Publisher: Springer Science & Business Media ISBN: 3662050188 Category : Mathematics Languages : en Pages : 526
Book Description
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.
Author: Jack Xu Publisher: UniCAD ISBN: 1695895576 Category : Mathematics Languages : en Pages : 470
Book Description
The second edition of this book builds all the code example within a single project by incorporating new advancements in C# .NET technology and open-source math libraries. It also uses C# Interactive Window to test numerical computations without compiling or running the complete project code. The second edition includes three new chapters, including "Plotting", Fourier Analysis" and "Math Expression Parser". As in the first edition, this book presents an in-depth exposition of the various numerical methods used in real-world scientific and engineering computations. It emphasizes the practical aspects of C# numerical methods and mathematical functions programming, and discusses various techniques in details to enable you to implement these numerical methods in your .NET application. Ideal for scientists, engineers, and students who would like to become more adept at numerical methods, the second edition of this book covers the following content: - Overview of C# programming. - The mathematical background and fundamentals of numerical methods. - plotting the computation results using a 3D chart control. - Math libraries for complex numbers and functions, real and complex vector and matrix operations, and special functions. - Numerical methods for generating random numbers and random distribution functions. - Various numerical methods for solving linear and nonlinear equations. - Numerical differentiation and integration. - Interpolations and curve fitting. - Optimization of single-variable and multi-variable functions with a variety of techniques, including advanced simulated annealing and evolutionary algorithms. - Numerical techniques for solving ordinary differential equations. - Numerical methods for solving boundary value problems. - Eigenvalue problems. - Fourier analysis. - mathematical expression parser and evaluator. In addition, this book provides testing examples for every math function and numerical method to show you how to use these functions and methods in your own .NET applications in a manageable and step-by-step fashion. Please visit the author's website for more information about this book at https://drxudotnet.com https://drxudotnet.com and https://gincker.com.
Author: Eleuterio F. Toro Publisher: Springer Science & Business Media ISBN: 366203915X Category : Technology & Engineering Languages : en Pages : 635
Book Description
High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.
Author: Helmut Brass Publisher: American Mathematical Soc. ISBN: 0821853619 Category : Mathematics Languages : en Pages : 376
Book Description
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.
Author: Ursula van Rienen Publisher: Springer Science & Business Media ISBN: 3642568025 Category : Computers Languages : en Pages : 387
Book Description
treated in more detail. They are just specimen of larger classes of schemes. Es sentially, we have to distinguish between semi-analytical methods, discretiza tion methods, and lumped circuit models. The semi-analytical methods and the discretization methods start directly from Maxwell's equations. Semi-analytical methods are concentrated on the analytical level: They use a computer only to evaluate expressions and to solve resulting linear algebraic problems. The best known semi-analytical methods are the mode matching method, which is described in subsection 2. 1, the method of integral equations, and the method of moments. In the method of integral equations, the given boundary value problem is transformed into an integral equation with the aid of a suitable Greens' function. In the method of moments, which includes the mode matching method as a special case, the solution function is represented by a linear combination of appropriately weighted basis func tions. The treatment of complex geometrical structures is very difficult for these methods or only possible after geometric simplifications: In the method of integral equations, the Greens function has to satisfy the boundary condi tions. In the mode matching method, it must be possible to decompose the domain into subdomains in which the problem can be solved analytically, thus allowing to find the basis functions. Nevertheless, there are some ap plications for which the semi-analytic methods are the best suited solution methods. For example, an application from accelerator physics used the mode matching technique (see subsection 5. 4).
Author: George Lindfield Publisher: Academic Press ISBN: 0128123702 Category : Technology & Engineering Languages : en Pages : 610
Book Description
The fourth edition of Numerical Methods Using MATLAB® provides a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors' approach is to integrate MATLAB® with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB®. MATLAB® graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature. The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB® to help researchers analyze a particular outcome. By using MATLAB® it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics. - Features many numerical algorithms, their fundamental principles, and applications - Includes new sections introducing Simulink, Kalman Filter, Discrete Transforms and Wavelet Analysis - Contains some new problems and examples - Is user-friendly and is written in a conversational and approachable style - Contains over 60 algorithms implemented as MATLAB® functions, and over 100 MATLAB® scripts applying numerical algorithms to specific examples
Author: Gwynne Evans
Author: Philip J. Davis
Author: Ernst Hairer
Author: Jack Xu
Author: Eleuterio F. Toro
Author: Helmut Brass
Author: Uri M. Ascher
Author: Ursula van Rienen
Author: Amir Wadi Al-Khafaji
Author: George Lindfield