Numerical Methods

Integral Deferred Correction Methods, Semi-implicit Methods, Splitting Methods

Integral Deferred Correction (IDC) methods are high order numerical time integrators whose structure leads to simple construction of arbitrary order integrators. IDC methods involve a low order prediction step and correction of the prediction to higher order. A key component is the solution of an error equation in integral form.

Certain modifications to IDC allow high order numerical solutions to multi-scale and/or nonlinear problems in plasma physics, such as the Vlasov-Poisson (VP) 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. Incorporation of split IDC with conservative semi-Lagrangian WENO interpolation results in well-resolved solutions to classic plasma physics problems such as Landau damping and two stream instability.