A semi-implicit form of spectral deferred corrections is used in a method of lines approach to
create a projection method that is sixth-order accurate in both time and space for simple …

Splitting-based time integration approaches such as fractional step, alternating direction
implicit, operator splitting, and locally one dimensional methods partition the system of …

We present modifications of the second-order Douglas stabilizing corrections method, which
is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a …

High-order semi-implicit Picard integral deferred correction (SIPIDC) methods have
previously been proposed for the time-integration of partial differential equations with two or …

An error analysis is presented for explicit partitioned Runge–Kutta methods and multirate
methods applied to conservation laws. The interfaces, across which different methods or …

Abstract Alternating Directions Implicit (ADI) integration is an operator splitting approach to
solve parabolic and elliptic partial differential equations in multiple dimensions based on …

In this paper we develop a set of time integrators of type fractional step Runge–Kutta
methods which generalize the time integrator involved in the classical Peaceman–Rachford …

A generic projection maps one vector to another such that their difference is a gradient field
and the projected vector does not have to be solenoidal. Via a commutator of Laplacian and …

Splitting-based time integration approaches such as fractional step, alternating direction
implicit, operator splitting, and locally one dimensional methods partition the system of …

We present modifications of the second-order Douglas stabilizing corrections method, which
is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a …