Numerical Methods for Ordinary Differential Equations

Initial Value Problems

Authors:

ISBN: 978-0-85729-147-9 (Print) 978-0-85729-148-6 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xiv

  2. No Access

    Book Chapter

    Pages 1-18

    ODEs—An Introduction

  3. No Access

    Book Chapter

    Pages 19-31

    Euler’s Method

  4. No Access

    Book Chapter

    Pages 33-42

    The Taylor Series Method

  5. No Access

    Book Chapter

    Pages 43-60

    Linear Multistep Methods—I: Construction and Consistency

  6. No Access

    Book Chapter

    Pages 61-73

    Linear Multistep Methods—II: Convergence and Zero-Stability

  7. No Access

    Book Chapter

    Pages 75-94

    Linear Multistep Methods—III: Absolute Stability

  8. No Access

    Book Chapter

    Pages 95-108

    Linear Multistep Methods—IV: Systems of ODEs

  9. No Access

    Book Chapter

    Pages 109-121

    Linear Multistep Methods—V: Solving Implicit Methods

  10. No Access

    Book Chapter

    Pages 123-134

    Runge–Kutta Method—I: Order Conditions

  11. No Access

    Book Chapter

    Pages 135-143

    Runge-Kutta Methods–II Absolute Stability

  12. No Access

    Book Chapter

    Pages 145-163

    Adaptive Step Size Selection

  13. No Access

    Book Chapter

    Pages 165-176

    Long-Term Dynamics

  14. No Access

    Book Chapter

    Pages 177-193

    Modified Equations

  15. No Access

    Book Chapter

    Pages 195-206

    Geometric Integration Part I—Invariants

  16. No Access

    Book Chapter

    Pages 207-223

    Geometric Integration Part II—Hamiltonian Dynamics

  17. No Access

    Book Chapter

    Pages 225-241

    Stochastic Differential Equations

  18. Back Matter

    Pages 243-271