Solving Ordinary Differential Equations II

Stiff and Differential-Algebraic Problems

Authors:

ISBN: 978-3-642-05220-0 (Print) 978-3-642-05221-7 (Online)

Table of contents (38 chapters)

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  1. Front Matter

    Pages I-XV

  2. Stiff Problems — One-Step Methods

    1. Front Matter

      Pages 1-1

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      Chapter

      Pages 2-14

      Examples of Stiff Equations

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      Chapter

      Pages 15-39

      Stability Analysis for Explicit RK Methods

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      Chapter

      Pages 40-50

      Stability Function of Implicit RK-Methods

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      Chapter

      Pages 51-70

      Order Stars

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      Chapter

      Pages 71-90

      Construction of Implicit Runge-Kutta Methods

    7. No Access

      Chapter

      Pages 91-101

      Diagonally Implicit RK Methods

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      Chapter

      Pages 102-117

      Rosenbrock-Type Methods

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      Chapter

      Pages 118-130

      Implementation of Implicit Runge-Kutta Methods

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      Chapter

      Pages 131-142

      Extrapolation Methods

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      Chapter

      Pages 143-166

      Numerical Experiments

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      Chapter

      Pages 167-179

      Contractivity for Linear Problems

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      Chapter

      Pages 180-200

      B-Stability and Contractivity

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      Chapter

      Pages 201-214

      Positive Quadrature Formulas and B-Stable RK-Methods

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      Chapter

      Pages 215-224

      Existence and Uniqueness of IRK Solutions

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      Chapter

      Pages 225-238

      B-Convergence

  3. Multistep Methods for Stiff Problems

    1. Front Matter

      Pages 239-239

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      Chapter

      Pages 240-249

      Stability of Multistep Methods

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      Chapter

      Pages 250-260

      “Nearly” A-Stable Multistep Methods

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      Chapter

      Pages 261-278

      Generalized Multistep Methods

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      Chapter

      Pages 279-299

      Order Stars on Riemann Surfaces

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      Chapter

      Pages 300-304

      Experiments with Multistep Codes

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