Abstract. In this paper, we construct high order semi-implicit integrators using integral deferred correction (IDC) to solve stiff initial value problems. The general framework for the construction of these semi-implicit methods uses uniformly distributed nodes and additive Runge-Kutta (ARK) integrators as base schemes inside an IDC framework, which we refer to as IDC-ARK methods. We establish under mild assumptions that, when an r th order ARK method is used to predict and correct the numerical solution, the order of accuracy of the IDC method increases by r for each IDC prediction and correction loop. Numerical experiments support the established theorems, and also indicate that higher order IDC-ARK methods present an efficiency advantage over existing implicit-explicit (IMEX) ARK schemes in some cases.

Abstract. Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in [Qiu and Christlieb, J. Comp. Phys., 2010] is very high (as high as ninth order). However, the temporal error is dominated by the operator splitting error, which is second order for Strang splitting. It is therefore important to overcome such low order splitting error, in order to have numerical algorithms that achieve higher orders of accuracy in both space and time. In this paper, we propose to use the integral deferred correction (IDC) method to reduce the splitting error. Specifically, the temporal order accuracy is increased by r with each correction loop in the IDC framework, where r = 1, 2 for coupling the first order splitting and the Strang splitting, respectively. The proposed algorithm is applied to the Vlasov-Poisson system, the guiding center model, and two dimensional incompressible flow simulations in the vorticity stream-function formulation. We show numerically that the IDC procedure can automatically increase the order of accuracy in time. We also investigate numerical stability of the proposed algorithm via performing Fourier analysis to a linear model problem.

Enhancing soil-protecting living cover over the winter is an important challenge in temperate row crop production. Th is note reports on novel fi ndings for cover crop seed priming, a process of controlled hydration and drying. Th e eff ects of seed priming over durations of 0, 2, 4, 8, 12, 24, and 36 h were evaluated for four species that varied in seed size and germination characteristics: cereal rye (Secale cereale L.), perennial ryegrass (Lolium perenne L.), hairy vetch (Vicia villosa Roth), and oriental mustard (Brassica juncea L.). A logistic function modeled response was used to quantify onset of germination, time to 50% germination (t 50 ), maximum germination rate, fi nal germination percentage (K), seedling emergence, and establishment in laboratory germination paper and soil core assays. Rye seed germinated rapidly regardless of priming treatment. Under the optimum environmental conditions of a laboratory germination assay, the smallest seeded cover crop, perennial ryegrass, was the only species to show a fi nal germination response that was higher in primed (86%) than untreated seed (78%). However, seed germination rates of three species were infl uenced by priming: 50% germination was reached 8, 6, and 9 h earlier in hairy vetch, mustard, and perennial ryegrass, respectively. Compacted soil assays showed that priming (24 h) improved seedling emergence by 36% and 57% for hairy vetch and perennial ryegrass, respectively, compared with untreated seed. Th ese results were consistent across experiment runs. Seed priming shows promise as a new technology for improving cover crop establishment in compacted soil.