Superconvergence for Galerkin Methods for the Two Point Boundary Problem Via Local Projections.
Superconvergence of external approximation for two-point boundary problems
The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.
Superconvergence of the gradient of finite element solutions
Sur la A-stabilité des méthodes de Runge-Kutta.
Sur le calcul de la partie principale d'un tore de bifurcation pour un système différentiel périodique
Symmetric parareal algorithms for hamiltonian systems
The parareal in time algorithm allows for efficient parallel numerical simulations of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available. In this article, we are concerned with the long time integration of Hamiltonian systems. Geometric, structure-preserving integrators are...
Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh,...
Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh,...
Symplectic phase flow approximation for the numerical integration of canonical systems.
Systémy algebro-diferenciálních rovnic
The application of a class of one-step methods to solve the initial value problem
The Application of Rosenbrock-Wanner Type Methods with Stepsize Control in Differential-Algebraic Equations.
The approximate Euler method for Lévy driven stochastic differential equations
The Approximation of Generalized Turning Points by Projection Methods with Superconvergence to the Critical Parameter.
The best argument for the parametric continuation of solutions of differential-algebraic equations.
The Convergence of Spline Collocation for Strongly Elliptic Equations on Curves.
The CUDA implementation of the method of lines for the curvature dependent flows
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
The direct dynamical problem of seismics for horizontally stratified media.
The Drazin inverse in multibody system dynamics.
The elimination of quantities and the solving of systems of transcendent equations by means of differential equations