Numerical methods for stiff equations and singular perturbation problems Willard L. Miranker. Mathematics and its applications 5; Mathematics and its applications Horwood ; Halsted Press.

Miranker, Willard L.:

ISBN 10: 9027711070 / ISBN 13: 9789027711076

Editore: Dordrecht, D Reidel [1981]., 1981

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Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 65 MIR 9789027711076 Sprache: Englisch Gewicht in Gramm: 550.

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Dati bibliografici

• Titolo: Numerical methods for stiff equations and singular perturbation problems Willard L. Miranker. Mathematics and its applications 5; Mathematics and its applications Horwood ; Halsted Press.
• Editore: Dordrecht, D Reidel [1981].
• Data di pubblicazione: 1981
• Lingua: Inglese
• ISBN 10: 9027711070
• ISBN 13: 9789027711076
• Rilegatura: Hardcover
• Peso: 550 grammi
• Cataloghi dei venditori:
  • SA MATHEMATIK

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Riassunto

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Contenuti

1. Introduction.- Summary.- 1.1. Stiffness and Singular Perturbations.- 1.1.1. Motivation.- 1.1.2. Stiffness.- 1.1.3. Singular Perturbations.- 1.1.4. Applications.- 1.2. Review of the Classical Linear Multistep Theory.- 1.2.1. Motivation.- 1.2.2. The Initial Value Problem.- 1.2.3. Linear Multistep Operators.- 1.2.4. Approximate Solutions.- 1.2.5. Examples of Linear Multistep Methods.- 1.2.6. Stability, Consistency and Convergence.- 2. Methods of Absolute Stability.- Summary.- 2.1. Stiff Systems and A-stability.- 2.1.1. Motivation.- 2.1.2. A-stability.- 2.1.3. Examples of A-stable Methods.- 2.1.4. Properties of A-stable Methods.- 2.1.5. A Sufficient Condition for A-stability.- 2.1.6. Applications.- 2.2. Notions of Diminished Absolute Stability.- 2.2.1. A (?)-stability.- 2.2.2. Properties of A(?)-stable Methods.- 2.2.3. Stiff Stability.- 2.3. Solution of the Associated Equations.- 2.3.1. The Problem.- 2.3.2. Conjugate Gradients and Dichotomy.- 2.3.3. Computational Experiments.- 3. Nonlinear Methods.- Summary.- 3.1. Interpolatory Methods.- 3.1.1. Certaine’s Method.- 3.1.2. Jain’s Method.- 3.2. Runge-Kutta Methods and Rosenbrock Methods.- 3.2.1. Runge-Kutta Methods with v-levels.- 3.2.2. Determination of the Coefficients.- 3.2.3. An Example.- 3.2.4. Semi-explicit Processes and the Method of Rosenbrock.- 3.2.5. A-stability.- 4 Exponential Fitting.- Summary.- 4.1. Exponential Fitting for Linear Multistep Methods.- 4.1.1. Motivation and Examples.- 4.1.2. Minimax fitting.- 4.1.3. An Error Analysis for an Exponentially Fitted F1.- 4.2. Fitting in the Matricial Case.- 4.2.1. The Matricial Multistep Method.- 4.2.2. The Error Equation.- 4.2.3. Solution of the Error Equation.- 4.2.4. Estimate of the Global Error.- 4.2.5. Specification of P.- 4.2.6. Specification of L and R.- 4.2.7. An Example.- 4.3. Exponential Fitting in the Oscillatory Case.- 4.3.1. Failure of the Previous Methods.- 4.3.2. Aliasing.- 4.3.3. An Example of Aliasing.- 4.3.4. Application to Highly Oscillatory Systems.- 4.4. Fitting in the Case of Partial Differential Equations.- 4.4.1. The Problem Treated.- 4.4.2. The Minimization Problem.- 4.4.3. Highly Oscillatory Data.- 4.4.4. Systems.- 4.4.5. Discontinuous Data.- 4.4.6. Computational Experiments.- 5. Methods of Boundary Layer Type.- Summary.- 5.1. The Boundary Layer Numerical Method.- 5.1.1. The Boundary Layer Formalism.- 5.1.2. The Numerical Method.- 5.1.3. An Example.- 5.2. The ?-independent Method.- 5.2.1. Derivation of the Method.- 5.2.2. Computational Experiments.- 5.3. The Extrapolation Method.- 5.3.1. Derivation of the Relaxed Equations.- 5.3.2. Computational Experiments.- 6. The Highly Oscillatory Problem.- Summary.- 6.1. A Two-time Method for the Oscillatory Problem.- 6.1.1. The Model Problem.- 6.1.2. Numerical Solution Concept.- 6.1.3. The Two-time Expansion.- 6.1.4. Formal Expansion Procedure.- 6.1.5. Existence of the Averages and Estimates of the Remainder.- 6.1.6. The Numerical Algorithm.- 6.1.7. Computational Experiments.- 6.2. Algebraic Methods for the Averaging Process.- 6.2.1. Algebraic Characterization of Averaging.- 6.2.2. An Example.- 6.2.3. Preconditioning.- 6.3. Accelerated Computation of Averages and an Extrapolation Method.- 6.3.1. The Multi-time Expansion in the Nonlinear Case.- 6.3.2. Accelerated Computation of $$\bar f$$.- 6.3.3. The Extrapolation Method.- 6.3.4. Computational Experiments: A Linear System.- 6.3.5. Discussion.- 6.4. A Method of Averaging.- 6.4.1. Motivation: Stable Functionals.- 6.4.2. The Problem Treated.- 6.4.3. Choice of Functionals.- 6.4.4. Representers.- 6.4.5. Local Error and Generalized Moment Conditions.- 6.4.6. Stability and Global Error Analysis.- 6.4.7. Examples.- 6.4.8. Computational Experiments.- 4.6.9. The Nonlinear Case and the Case of Systems.- 7. Other Singularly Perturbed Problems.- Summary.- 7.1. Singularly Perturbed Recurrences.- 7.1.1. Introduction and Motivation.- 7.1.2. The Two-time Formalism for Recurrences.- 7.1.3. The Averaging Procedure.- 7.1.4. The Linear Case.- 7.1.5. Additional Applications.- 7.2. Singularly Perturbed Boundary Value Problems.- 7.2.1. Introduction.- 7.2.2. Numerically Exploitable Form of the Connection Theory.- 7.2.3. Description of the Algorithm.- 7.2.4. Computational Experiments.- References.