Numerical Methods for Stiff Equations and Singular Perturbation Problems - A. Miranker

Numerical Methods for Stiff Equations and Singular Perturbation Problems

and Singular Perturbation Problems

(Autor)

Buch | Softcover
204 Seiten
2001 | Softcover reprint of the original 1st ed. 1981
Springer-Verlag New York Inc.
978-1-4020-0298-4 (ISBN)
53,49 inkl. MwSt
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; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory;
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.

1. Introduction.- Summary.- 1.1. Stiffness and Singular Perturbations.- 1.2. Review of the Classical Linear Multistep Theory.- 2. Methods of Absolute Stability.- Summary.- 2.1. Stiff Systems and A-stability.- 2.2. Notions of Diminished Absolute Stability.- 2.3. Solution of the Associated Equations.- 3. Nonlinear Methods.- Summary.- 3.1. Interpolatory Methods.- 3.2. Runge-Kutta Methods and Rosenbrock Methods.- 4 Exponential Fitting.- Summary.- 4.1. Exponential Fitting for Linear Multistep Methods.- 4.2. Fitting in the Matricial Case.- 4.3. Exponential Fitting in the Oscillatory Case.- 4.4. Fitting in the Case of Partial Differential Equations.- 5. Methods of Boundary Layer Type.- Summary.- 5.1. The Boundary Layer Numerical Method.- 5.2. The ?-independent Method.- 5.3. The Extrapolation Method.- 6. The Highly Oscillatory Problem.- Summary.- 6.1. A Two-time Method for the Oscillatory Problem.- 6.2. Algebraic Methods for the Averaging Process.- 6.3. Accelerated Computation of Averages and an Extrapolation Method.- 6.4. A Method of Averaging.- 7. Other Singularly Perturbed Problems.- Summary.- 7.1. Singularly Perturbed Recurrences.- 7.2. Singularly Perturbed Boundary Value Problems.- References.

Erscheint lt. Verlag 30.11.2001
Reihe/Serie Mathematics and Its Applications ; 5
Mathematics and Its Applications ; 5
Zusatzinfo XIV, 204 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 1-4020-0298-X / 140200298X
ISBN-13 978-1-4020-0298-4 / 9781402002984
Zustand Neuware
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