Abst rac t . The Crank-Nicolson scheme is widely used to solve numerically the diffusion equation, because of its good stability properties. It is, however, ill-behaved when large time-steps are used: the short wave-lengths may happen to be less damped than the long ones. A detailed analysis of this flaw is performed and an Mternative scheme is proposed, which removes this difficulty while pres...

An algorithm allowing a fast solution of stationary and time dependent 1-d diffusion problems for the case of finite ionization and recombination rates is presented. Results of numerical computations and an analytic stability analysis show its unconditional stability. The computational effort involved rises only linearly with the number of ionization stages included. An application to the diffu...

After stating an abstract convergence result for the parareal algorithm used in the parallelization in time of general partial differential equations, we analyze the stability and convergence properties of the algorithm for equations with constant coefficients. We show that suitably damping coarse schemes ensure unconditional stability of the parareal algorithm and analyze how the regularity of...

Abstract In this article, we present a second-order in time implicit-explicit (IMEX) local discontinuous Galerkin (LDG) method for computing the Cahn-Hilliard equation, which describes the phase separation phenomenon. It is well-known that the Cahn-Hilliard equation has a nonlinear stability property, i.e., the free-energy functional decreases with respect to time. The discretized Cahn-Hilliard...

This paper presents a coupling method in order to establish force-feedback user interaction with a micromanipulator. The presented control scheme design is based on stability considerations and, hence, allows unconditional stable operation independently on the haptic interface, micromanipulator and scaling ratios on force and position. Experimental comparison of proposed coupling with a common ...

A semi-implicit, lowest order finite element scheme for the approximation of wave maps into smooth or convex surfaces is devised and its stability is analyzed. Convergence is established for the case of the unit sphere as a target manifold, which is unconditional in case of (2+1) Minkowski space. Numerical experiments illustrate the theoretical results.

A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numeri...

The wave equation with attenuation due to a linear friction is approximated by a new mixed nite element method which allows one to use diierent grids and basis functions at diierent times when necessary. This method enables one to track sharp moving wave fronts more eeciently and accurately. Error estimates with optimal convergent rates are established. Unconditional stability is also proved fo...