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...
Partitioned Adaptive Runge-Kutta Methods and Their Stability.
Partitioned Adaptive Runge-Kutta Methods for the Solution of Nonstiff and Stiff Systems.
Partitioned Runge-Kutta Methods with Stiffness Detection and Stepsize Control.
Perturbed Collocation and Runge-Kutta Methods.
Phase portraits of planar vector fields: Computer proofs.
Piecewise Polynomial Taylor Methods for Initial Value Problems.
Pointwise Lower and Upper Bounds for Eigenfunctions of Ordinary Differential Operators.
Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems
In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of the mixed finite element space.
Power bounded prolongations and Picard-Lindelöf iteration.
Practical method for solving differential equations and their systems bu means of Taylor series
Practice of operator relationships in symbolical calculus.
Programming of differential equations with singularitiens of the type in using the extension to power series
Projection Methods and Singular Two Point Boundary Value Problems.