Download or read book Exponentially Convergent Algorithms for Abstract Differential Equations written by Ivan Gavrilyuk and published by Springer Science & Business Media. This book was released on 2011-07-17 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.
Download or read book Recent Developments in Structure Preserving Algorithms for Oscillatory Differential Equations written by Xinyuan Wu and published by Springer. This book was released on 2018-04-19 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.
Download or read book An Exponential Convergent Algorithm for Nonlinear Differential Equations in Banach Spaces written by Ivan P. Gavriljuk and published by . This book was released on 2005 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Analysis and Applications written by Vadim Adamyan and published by Springer Science & Business Media. This book was released on 2009-08-29 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structure Preserving Algorithms for Oscillatory Differential Equations written by Xinyuan Wu and published by Springer Science & Business Media. This book was released on 2013-02-02 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations. The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.
Download or read book Computational Methods in Applied Mathematics written by and published by . This book was released on 2006 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Difference Equations written by Saber N. Elaydi and published by CRC Press. This book was released on 1998-01-29 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent surge in research activity in difference equations and applications has been driven by the wide applicability of discrete models to such diverse fields as biology, engineering, physics, economics, chemistry, and psychology. The 68 papers that make up this book were presented by an international group of experts at the Second International Conference on Difference Equations, held in Veszprém, Hungary, in August, 1995. Featuring contributions on such topics as orthogonal polynomials, control theory, asymptotic behavior of solutions, stability theory, special functions, numerical analysis, oscillation theory, models of vibrating string, models of chemical reactions, discrete competition systems, the Liouville-Green (WKB) method, and chaotic phenomena, this volume offers a comprehensive review of the state of the art in this exciting field.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion Algorithm And Models For Anomalous Diffusion written by Weihua Deng and published by World Scientific. This book was released on 2019-01-22 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.
Download or read book An Exponentially Convergent and Finite Algorithm for Linear Inequalities written by Yu-Chi Ho and published by . This book was released on 1964 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exponentially convergent and finite algorithm is presented which provides a rule of procedure for solving a fundamental problem in pattern classification, threshold switching theory, and mathematical programming. This problem is finding the m-vector x, such that Ax> 0, where A is a given Nxm matrix with N” m.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Proceedings of the 2011 2nd International Congress on Computer Applications and Computational Science written by Ford Lumban Gaol and published by Springer Science & Business Media. This book was released on 2012-02-23 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest inventions in computer technology influence most of human daily activities. In the near future, there is tendency that all of aspect of human life will be dependent on computer applications. In manufacturing, robotics and automation have become vital for high quality products. In education, the model of teaching and learning is focusing more on electronic media than traditional ones. Issues related to energy savings and environment is becoming critical. Computational Science should enhance the quality of human life, not only solve their problems. Computational Science should help humans to make wise decisions by presenting choices and their possible consequences. Computational Science should help us make sense of observations, understand natural language, plan and reason with extensive background knowledge. Intelligence with wisdom is perhaps an ultimate goal for human-oriented science. This book is a compilation of some recent research findings in computer application and computational science. This book provides state-of-the-art accounts in Computer Control and Robotics, Computers in Education and Learning Technologies, Computer Networks and Data Communications, Data Mining and Data Engineering, Energy and Power Systems, Intelligent Systems and Autonomous Agents, Internet and Web Systems, Scientific Computing and Modeling, Signal, Image and Multimedia Processing, and Software Engineering.
Download or read book Structure Preserving Algorithms for Oscillatory Differential Equations II written by Xinyuan Wu and published by Springer. This book was released on 2016-03-03 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods. The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and scientists investigating oscillatory systems, as well as for teachers and students who are interested in structure-preserving algorithms for differential equations.
