Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirable time-step restrictions when applied to convection-diffusion problems, unless diffusion strongly dominates and an appropriate BDF-based scheme is selected (Ascher et al., 1995). In this paper, we develop Runge-Kut...

It is shown that for a parabolic problem with maximal Lp-regularity (for 1 < p < ∞), the time discretization by a linear multistep method or Runge–Kutta method has maximal `p-regularity uniformly in the stepsize if the method is A-stable (and satisfies minor additional conditions). In particular, the implicit Euler method, the Crank–Nicolson method, the second-order backward difference formula ...

Abstract: Transient analysis is an important circuit simulation technique. The circuit model, which is a system of differential-algebraic equations, is solved for a given initial condition using numerical time integration techniques. Multirate methods are efficient if the dynamical behaviour of the circuit model is not uniform. This paper deals with the analysis and control of the discretizatio...

The concepts of stability regions, Aand A(α)-stability – albeit based on scalar models – turned out to be essential for the identification of implicit methods suitable for the integration of stiff ODEs. However, for multistep methods, knowledge of the stability region provides no information on the quantitative stability behavior of the scheme. In this paper we fill this gap for the important c...

The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to instationary problems can, e.g., be done by backward difference formulae (BDF) or diagonally implicit Runge-Kutta (DIRK) methods. In this publication, we investigate the use of embedded DIRK methods in an HDG solver, including the use of adapti...

I. Fasted dog serum non-ester&d fatty acid (NEFA) levels were elevated to and 34 hours after administration of a diabetogenic protein (BDF) isolated from bovine adenohypoph+L 2. The fasting serum NEFA were elevated in spite of the presence of normal or high glucose and insulin Icvels. 3. After oral glucase administration to BDF-treated animals, a fall of serum NEFA paralleled inversely the incr...

We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate space and time. In considered setting, physical domain that evolves essentially arbitrarily through time-independent computational background represented by level set function. For time discretization, application standard stepping schemes ...