A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusiondissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.

We extend our recent work on higher-order time integration of Richards' equation to layered heterogeneous porous media, using a diierential-algebraic-equation-based method of lines (DAE/MOL) approach. We show that the DAE/MOL approach is robust and eecient compared to standard low-order time integration methods for heterogeneous media. We also show the advantage of using an integral representat...

The parareal algorithm is a method to solve time-dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on new convergence results that show supe...

We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE can be decomposed into several pieces and each of them is integrable. This class of integrators are explicit, simple to implement and preserve structural pr...

DESPITE THE PLETHORA OF RESEARCH ON THE ROLE of tonality and meter in music perception, there is little work on how these fundamental properties function together. The most basic question is whether the two hierarchical structures are correlated – that is, do metrically stable positions in the measure preferentially feature tonally stable pitches, and do tonally stable pitches occur more often ...

New explicit Runge-Kutta methods are presented for the time integration of the incompressible Navier-Stokes equations. The differential-algebraic nature of these equations requires that additional order conditions are satisfied compared to the classical order conditions for ordinary differential equations. The methods presented in this work are high-order accurate for both velocity and pressure...

This report analyzes a partitioned time stepping algorithm, meaning a non-iterative, domain decomposition method, which allows different time steps in the fluid region and the porous region for the fully evolutionary Stokes-Darcy problem. The method presented requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a time step restriction of the form 4...