SAYAS NUMERICS SEMINAR     Register to attend talk
May 4, 2021 at 3:30pm (Eastern Time)

Time stepping differential equations with a posteriori error estimation

Emil Constantinescu
Argonne National Laboratory

When solving ordinary differential equations one typically estimates or attempts to control the local truncation error (called local error). In practice, a posteriori error also known as "global error" is deemed to be too expensive to estimate.

In this talk we introduce a new optimal time-stepping method with affordable built-in a posteriori error estimates. These methods can be cast as general linear time stepping schemes and provide pointwise asymptotically-correct local and global error estimates. We analyze their convergence, order conditions, and barriers. We also illustrate situations in which the more common local error estimation is not a reliable error measure.