A Numerical Study of a Perturbation Theory Model - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Numerical Study of a Perturbation Theory Model write by Henry Joseph Happ. This book was released on 1973. A Numerical Study of a Perturbation Theory Model available in PDF, EPUB and Kindle.
Perturbation theory for linear operators
Perturbation theory for linear operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbation theory for linear operators write by Tosio Kato. This book was released on 2013-06-29. Perturbation theory for linear operators available in PDF, EPUB and Kindle.
Perturbation Theory for Matrix Equations
Perturbation Theory for Matrix Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbation Theory for Matrix Equations write by M. Konstantinov. This book was released on 2003-05-20. Perturbation Theory for Matrix Equations available in PDF, EPUB and Kindle. The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis. In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds. Key features: • The first book in this field • Can be used by a variety of specialists • Material is self-contained • Results can be used in the development of reliable computational algorithms • A large number of examples and graphical illustrations are given • Written by prominent specialists in the field
Testing Higher-Order Lagrangian Perturbation Theory Against Numerical Simulation. 1
Testing Higher-Order Lagrangian Perturbation Theory Against Numerical Simulation. 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Testing Higher-Order Lagrangian Perturbation Theory Against Numerical Simulation. 1 write by National Aeronautics and Space Administration (NASA). This book was released on 2018-07-12. Testing Higher-Order Lagrangian Perturbation Theory Against Numerical Simulation. 1 available in PDF, EPUB and Kindle. We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the ons...
A First Look at Perturbation Theory
A First Look at Perturbation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A First Look at Perturbation Theory write by James G. Simmonds. This book was released on 2013-07-04. A First Look at Perturbation Theory available in PDF, EPUB and Kindle. Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.
