Numerical solution of ordinary differential equations
MTH 452/552

MWF 10:00-10:50
Winter 2022

Outline

Last modified: Mon Jan 03 11:28:38 PST 2022

Note: [AP] refers to Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by Ascher and Petzold.
Otherwise, chapters and § refer to Finite Difference Methods for Ordinary and Partial Differential Equations by Randy LeVeque.

  1. Finite Difference Approximations to Derivatives
    • § 1.1: Truncation Error (Order of Accuracy)
    • § 1.2,1.5: Undetermined Coefficients
    • § 1.3,1.4: Higher Order Derivatives
  2. Background on ODE Theory
    • IVP vs BVP
    • § 5.2: Existence, Uniqueness, Well-posedness
    • [AP] Chapter 2: Stability of Solutions (Stability Region)
  3. Numerical Methods for ODEs
    • § 5.3-5.6: Taylor Series Methods
    • § 5.7: Multistage Methods
    • § 5.8-5.9: Multistep Methods
    • § 5.9.4: Predictor-Corrector Methods
  4. Analysis of Methods
    • § 5.9.1: Consistency
    • § 6.1-6.3: Convergence
    • § 6.4: Zero-stability
    • Chapter 7: Absolute Stability (Absolute Stability Region)
  5. Chapter 8: Stiff ODEs