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Fundamentals of Numerical Computation

  • Home
  • Introduction
  • Square linear systems
  • Overdetermined linear systems
  • Roots of nonlinear equations
  • Piecewise interpolation
  • Initial-value problems for ODEs
  • Review: Linear algebra
  • All demo notebooks
    • Chapter 1 (Introduction)
    • Chapter 2 (Linear systems)
    • Chapter 3 (Least squares)
    • Chapter 4 (Rootfinding)
    • Chapter 5 (Piecewise)
    • Chapter 6 (IVPs)
      • Numerical IVP solution
      • Using an IVP solution
      • IVP with singularity
      • Conditioning of IVPs
      • Convergence of Euler’s method
      • Matrix exponential
      • Predator-prey system
      • Convergence of RK methods
      • Adaptive RK
      • Adaptivity at a singularity
      • Convergence of AB4
      • Accuracy isn’t everything
      • Instability in a multistep method
  • References
  • Index
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Chapter 6 (IVPs)¶

  • Numerical IVP solution

  • Using an IVP solution

  • IVP with singularity

  • Conditioning of IVPs

  • Convergence of Euler’s method

  • Matrix exponential

  • Predator-prey system

  • Convergence of RK methods

  • Adaptive RK

  • Adaptivity at a singularity

  • Convergence of AB4

  • Accuracy isn’t everything

  • Instability in a multistep method

Adaptive integration Numerical IVP solution

By Tobin A. Driscoll and Richard J. Braun
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