Download or read book Numerical Methods for Stiff Equations and Singular Perturbation Problems written by A. Miranker and published by Springer. This book was released on 2001-12-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from It isn't that they can't see the the right end and begin with the solution. It is that they can't see the problem. answers. Then, one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers' G. K. Chesterton, The scandal of in R. Van Gulik's The Chinese Maze Father Brown "The point ofa pin" Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Download or read book Numerical Methods for Stiff Equations and Singular Perturbation Problems written by A. Miranker and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from It isn't that they can't see the the right end and begin with the solution. It is that they can't see the problem. answers. Then, one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers' G. K. Chesterton, The scandal of in R. Van Gulik's The Chinese Maze Father Brown "The point ofa pin" Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Download or read book Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition written by John J H Miller and published by World Scientific. This book was released on 2012-02-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Download or read book Numerical Methods For Stiff Equations And Singular Perturbation Problems written by W.L. Miranker and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.
Download or read book Numerical Analysis of Singular Perturbation Problems written by P. W. Hemker and published by . This book was released on 1979 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 14 lectures by the invited speakers and 14 shorter contributions from the other speakers (pref.)
Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer. This book was released on 1987 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.
Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by Academic Press. This book was released on 2014-05-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.
Download or read book Stiff Differential Systems written by Ralph Willoughby and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in these proceedings were presented at an Inter national Symposium on Stiff Differential Systems, which was held at the Hotel Quellenhof, Wildbad, Federal Republic of Germany, October 4-6, 1973. The sumposium was organized by IBM Germany and sponsored by the IBM World Trade Corporation. On behalf of all the participants we wish to express our appreciation to the sponsors and organizers for their generous support,particularly to Dr. G. HUbner, representing Scientific Relations, IBM Germany, and Dr. G. Kozak, representing IBM World Trade Headquarters, New York. The purpose of the conference was to provide an intensive treatment of all apsects of a difficult problem class, stiff differential systems. Some major fields of interest of attendees and contributors are: 1) Modeling and problem solving in scien tific and technological applications, 2) Qualitative theory of stiff systems, 3) Numerical Analysis, including design, valida tion, and comparison of algorithms, as well as error and stability analysis, and 4) Computer Science, in particular problem-oriented programming languages, program packages, and applications-oriented computer architecture.
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1988-01-01 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Download or read book Numerical Methods for Stiff Equations and Singular Perturbation Problems written by A. Miranker and published by Springer. This book was released on 1980-11-30 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from It isn't that they can't see the the right end and begin with the solution. It is that they can't see the problem. answers. Then, one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers' G. K. Chesterton, The scandal of in R. Van Gulik's The Chinese Maze Father Brown "The point ofa pin" Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Download or read book The Computational Theory of Stiff Differential Equations written by Willard L. Miranker and published by . This book was released on 1976 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Stiff Ordinary Differential Equations written by Leon Lapidus and published by . This book was released on 1977 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis is presented for alternate numerical techniques for solving stiff ordinary differential equations. These techniques include a singular perturbation or pseudo-steady-state method and an imbedded, error-monitoring semi-implicit Runge-Kutta method. Extensive numerical experience on equations which are linear/nonlinear, small/large dimensional, and moderately/strongly stiff reveals that the singular perturbation method is most efficient for very stiff problems while the imbedded Runge-Kutta method is superb over a wide range of stiffness. (Author).
Download or read book Numerical Solution of Stiff and Singularly Perturbed Problems written by A. M. Nagy and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years much attention has been given to the numerical solution of ODEs. Of particular interest has been the solution of singularly perturbed and stiff problems. These types of problems arise in various fields of science and engineering such as fluid mechanics, physics, chemistry, mechanics, chemical reactor theory, convection diffusion processes, optimal control and other branches of applied mathematics. Singular perturbation problems depend on the presence of a small, positive parameter which provides a multi-scale character to the solution. That is the solution varies very rapidly in some parts of the region of integration (layers) and varies slowly in other parts. Stiffness is a property of the differential problem that makes slow and expensive the computation of the numerical solution using classical explicit methods. In this work, we present some numerical methods for solving IVPs and BVBs. Moreover, we give numerical solutions of Volterra integral and integro-differential equations. This book is high recommended to both postgraduate students and researchers in a wide variety of applications.
Download or read book The Numerical Solution of Boundary Value Problems for Stiff Differential Equations written by Joseph E. Flaherty and published by . This book was released on 1975 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical solution of boundary value problems for certain stiff ordinary differential equations is studied. The methods developed use singular perturbation theory to construct approximate numerical solutions which are valid asymptotically; hence, they have the desirable feature of becoming more accurate as the equations become stiffer. Several numerical examples are presented which demonstrate the effectiveness of these methods.
Download or read book Stiff Computation written by Richard C. Aiken and published by Oxford University Press, USA. This book was released on 1985 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Haar Wavelets written by Ülo Lepik and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
