Applied Mathematics Seminar: “Integral Deferred Correction Methods for Multi-scalre and Nonlinear Problems”

Monday April 15, 2019 at 4:00 PM in Yost 306

Speaker: Maureen M. Morton, Stark State College (


Integral Deferred Correction (IDC) methods are high order numerical time integrators whose structure leads to simple construction of arbitrary order integrators. High order numerical time
integrators, such as IDC, provide a valuable partnership with existing or new high order spatial methods. They ensure that results in both space and time attain similar quality, and neither limits the other. IDC methods involve a low order prediction step and correction of the prediction through solving an error equation. Certain modifications to IDC allow high order numerical solutions to multi-scale and/or nonlinear problems in plasma physics, such as the Vlasov-Poisson system. These modifications include incorporating semi-implicit methods to solve an IVP (arising from method of lines discretization) with a stiff and nonstiff term, or employing operator splitting into IDC’s prediction and correction steps. Such high order IDC methods are efficient when compared with Runge-Kutta methods. Also, despite introducing a CFL condition comparable to Eulerian methods, split IDC in time with conservative semi-Lagrangian WENO interpolation in space proves effective at preserving the expected physical properties in classic plasma physics problems.

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