Deferred correction is a well-established method for incrementally increasing the order of
accuracy of a numerical solution to a set of ordinary differential equations. Because …

In this work we discuss a class of defect correction methods which is easily adapted to
create parallel time integrators for multicore architectures and is ideally suited for develo** …

The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-
order collocation solution to an ODE by performing a series of correction sweeps using a low …

Spectral deferred correction (SDC) methods for solving ordinary differential equations
(ODEs) were introduced by Dutt, Greengard and Rokhlin (2000). It was shown in that paper …

The deferred correction (DeC) is an iterative procedure, characterized by increasing the
accuracy at each iteration, which can be used to design numerical methods for systems of …

Spectral deferred correction methods for solving stiff ODEs are known to converge
reasonably fast towards the collocation limit solution on equidistant grids, but show a less …

In this work, we describe the implementation of an arbitrarily high-order hybrid solver for
linear, kinetic, radiative transport equations. The hybrid method is derived from a splitting of …

High-order adaptive methods for fractional differential equations are proposed. The methods
rely on a kernel compression scheme for the approximation and localization of the history …

Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/
interpolation strategies have been applied to kinetic simulations. For example, the order of …

Parallel across the method time integration can provide small scale parallelism when
solving initial value problems. Spectral deferred corrections (SDCs) with a diagonal …