Numerical Stability

Introduction to Numerical Analysis  eBooks & eLearning

Posted by AvaxGenius at June 18, 2024
Introduction to Numerical Analysis

Introduction to Numerical Analysis by J. Stoer , R. Bulirsch
English | PDF | 1980 | 618 Pages | ISBN : N/A | 54 MB

This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda­ tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom­ pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d­ ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Introduction to Numerical Analysis  eBooks & eLearning

Posted by AvaxGenius at June 18, 2024
Introduction to Numerical Analysis

Introduction to Numerical Analysis by J. Stoer , R. Bulirsch
English | PDF | 1980 | 618 Pages | ISBN : N/A | 54 MB

This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda­ tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom­ pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d­ ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Repost)  eBooks & eLearning

Posted by AvaxGenius at Dec. 10, 2020
Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Repost)

Numerical Solution of Stochastic Differential Equations with Jumps in Finance by Eckhard Platen
English | PDF | 2010 | 868 Pages | ISBN : 3642120571 | 18 MB

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992).

Numerical Matrix Analysis: Linear Systems and Least Squares (Repost)  eBooks & eLearning

Posted by Specialselection at Feb. 22, 2014
Numerical Matrix Analysis: Linear Systems and Least Squares (Repost)

Ilse Ipsen, "Numerical Matrix Analysis: Linear Systems and Least Squares"
English | 2009-07-02 | ISBN: 0898716764 | 142 pages | PDF | 1.2 mb
Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB

Dimitri Breda, "Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB"
English | ISBN: 1493921061 | 2015 | 172 pages | PDF | 4 MB

Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB  eBooks & eLearning

Posted by AvaxGenius at May 12, 2018
Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB

Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB By Dimitri Breda
English | PDF,EPUB | 2015 | 162 Pages | ISBN : 1493921061 | 7.87 MB

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra.
Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB (Repost)

Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB By Dimitri Breda
English | PDF,EPUB | 2015 | 162 Pages | ISBN : 1493921061 | 7.87 MB

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra.
Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB (Repost)

Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB By Dimitri Breda
English | PDF,EPUB | 2015 | 162 Pages | ISBN : 1493921061 | 7.87 MB

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra.

Numerical Matrix Analysis: Linear Systems and Least Squares (Repost)  eBooks & eLearning

Posted by step778 at Nov. 17, 2017
Numerical Matrix Analysis: Linear Systems and Least Squares (Repost)

, "Numerical Matrix Analysis: Linear Systems and Least Squares"
2009 | pages: 142 | ISBN: 0898716764 | PDF | 1,2 mb

Computational Plasma Science: Physics and Selected Simulation Examples  eBooks & eLearning

Posted by AvaxGenius at May 10, 2023

Computational Plasma Science: Physics and Selected Simulation Examples

Computational Plasma Science: Physics and Selected Simulation Examples by Shigeo Kawata
English | PDF EPUB (True) | 2023 | 299 Pages | ISBN : 9819911362 | 58.4 MB

The book presents fundamentals of plasma physics with rich references and computational techniques in a concise manner. It particularly focuses on introductions to numerical simulation methods in plasma physics, in addition to those to physics and mathematics in plasma physics. It also presents the fundamentals of numerical methods, which solve mathematical models of plasmas, together with examples of numerical results. A discretization method, the so-called finite difference method, is introduced for particle-in-cell methods and fluid codes, which have been widely employed in plasma physics studies. In addition to the introduction to numerical solutions, it also covers numerical stability. The instabilities and numerical errors significantly influence the results, and for correct results, great efforts are required to avoid such numerical artifacts. The book also carefully discusses the numerical errors, numerical stability, and uncertainty in numerical computations.