Optimale Fehlerabschätzungen mit dualen Funktionalen bei semilineraen Randwertaufgaben gewöhnlicher Differentialgleichungen.
Optimale Runge-Kutta-Verfahren der Ordnung 2 und 3.
Optimale Verfahren zur numerischen Integration von Anfangswertproblemen.
Optimally stable fifth-order integration methods: A numerical approach.
Optimum error estimates for finite-difference methods
Order and Stepsize Control in Extrapolation Methods
Order Conditions for Numerical Methods for Partitioned Ordinary Differential Equations.
Order conditions for partitioned Runge-Kutta methods
We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential equations.
Order Conditions for Rosenbrock Type Methods.
Order results for Rosenbrock type methods on classes of stiff equations.
Oscillateurs harmoniques faiblement perturbés : l'algorithme numérique des «pas de géants»
Overimplicit methods for the solution of evolution problems
Overimplicit multistep methods
Parallel algorithms for initial and boundary value problems for linear ordinary differential equations and their systems
Parallel method for initial value problems for linear ordinary differential equations: speed up estimation
Parameter-uniform fitted mesh method for quasilinear differential equations with boundary layers.
Parameter-uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior.
Parameter-uniform fitted operator B-spline collocation method for self-adjoint singularly perturbed two-point boundary value problems.
Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...
Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...