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.
Inhaltsverzeichnis
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.
