New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration
DOWNLOAD
Download New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration
DOWNLOAD
Author : Richard Mikaël Slevinsky
language : en
Publisher:
Release Date : 2011
New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration written by Richard Mikaël Slevinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Differential calculus categories.
New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration
DOWNLOAD
Author : Richard Mikael Slevinsky
language : en
Publisher:
Release Date : 2013
New Formulae For Higher Order Derivatives And A New Algorithm For Numerical Integration written by Richard Mikael Slevinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Geometric Numerical Integration
DOWNLOAD
Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Geometric Numerical Integration written by Ernst Hairer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Methods Of Numerical Integration
DOWNLOAD
Author : Philip J. Davis
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Methods Of Numerical Integration written by Philip J. Davis and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Construction Of Integration Formulas For Initial Value Problems
DOWNLOAD
Author : P.J. Van Der Houwen
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Construction Of Integration Formulas For Initial Value Problems written by P.J. Van Der Houwen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
Construction of Integration Formulas for Initial Value Problems provides practice-oriented insights into the numerical integration of initial value problems for ordinary differential equations. It describes a number of integration techniques, including single-step methods such as Taylor methods, Runge-Kutta methods, and generalized Runge-Kutta methods. It also looks at multistep methods and stability polynomials. Comprised of four chapters, this volume begins with an overview of definitions of important concepts and theorems that are relevant to the construction of numerical integration methods for initial value problems. It then turns to a discussion of how to convert two-point and initial boundary value problems for partial differential equations into initial value problems for ordinary differential equations. The reader is also introduced to stiff differential equations, partial differential equations, matrix theory and functional analysis, and non-linear equations. The order of approximation of the single-step methods to the differential equation is considered, along with the convergence of a consistent single-step method. There is an explanation on how to construct integration formulas with adaptive stability functions and how to derive the most important stability polynomials. Finally, the book examines the consistency, convergence, and stability conditions for multistep methods. This book is a valuable resource for anyone who is acquainted with introductory calculus, linear algebra, and functional analysis.
New Developments Of Newton Type Iterations For Solving Nonlinear Problems
DOWNLOAD
Author : Tugal Zhanlav
language : en
Publisher: Springer Nature
Release Date :
New Developments Of Newton Type Iterations For Solving Nonlinear Problems written by Tugal Zhanlav and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Numerical Integration Of Space Fractional Partial Differential Equations
DOWNLOAD
Author : Younes Salehi
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-12-06
Numerical Integration Of Space Fractional Partial Differential Equations written by Younes Salehi and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-06 with Mathematics categories.
Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: •Vol 1: Introduction to Algorithms and Computer Coding in R •Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: •Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions •Fisher-Kolmogorov SFPDE •Burgers SFPDE •Fokker-Planck SFPDE •Burgers-Huxley SFPDE •Fitzhugh-Nagumo SFPDE. These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order ?? with 1 ≤ ?? ≤ 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).
A Concise Introduction To Geometric Numerical Integration
DOWNLOAD
Author : Sergio Blanes
language : en
Publisher: CRC Press
Release Date : 2017-11-22
A Concise Introduction To Geometric Numerical Integration written by Sergio Blanes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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.
Numerical Methods
DOWNLOAD
Author : George Em Karniadakis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-04-15
Numerical Methods written by George Em Karniadakis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-15 with Mathematics categories.
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.
Numerical Integration Of Space Fractional Partial Differential Equations
DOWNLOAD
Author : Younes Salehi
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-11-27
Numerical Integration Of Space Fractional Partial Differential Equations written by Younes Salehi and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-27 with Mathematics categories.
Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.