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[01007] Stability & Accuracy of Free-Parameter Multistep Methods for 1st & 2nd-order IVPs

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @E505
  • Type : Contributed Talk
  • Abstract : Dahlquist's First Stability Barrier limits the order of stable $k$-step multistep methods, allowing us to add free parameters. Within the parameter domain where a $k$-step family of methods is stable, we explore the parameters' effect on error and stability domains. For first-order IVP's, we investigate explicit methods for $k=2,3$ and implicit methods for $k=3,4$, generalizing Adams & BDF methods. For second-order IVP's, we analyze explicit and implicit methods for $k=3,4$, generalizing Störmer & Cowell methods.
  • Classification : 65L06, 65L07, 65L20
  • Author(s) :
    • Michelle Ghrist (Gonzaga University)
    • Ben Lombardi (Gonzaga University)
    • Alana Marie Dillinger (Twin Cities in Motion)