Transient noise analysis means time domain simulation of noisy electronic circuits. We consider mathematical models where the noise is taken into account by means of sources of Gaussian white noise that are added to the deterministic network equations, leading to systems of stochastic differential algebraic equations (SDAEs). A crucial property of the arising SDAEs is the large number of small ...

We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the second-order Gear’s extrapolation approach. The second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algor...

This paper presents a class of parallel numerical integration methods for stiff systems of ordinary differential equations which can be partitioned into loosely coupled sub-systems. The formulas are called decoupled backward differentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagonal sub-system. With one or several sub-systems allo...

A model is presented for stability for an extension of linear multistep methods for stiff ordinary differential equations. The method is based on a prediction followed by a fixed number of corrections obtained by a Newton scheme with inexact Jacobian matrix. The impact on stability of error in the matrix over a broad range of linear, constant coefficient equations is modeled. The model provides...

The compressible Navier-Stokes (NS) equations are spatially discretized with the discontinuous Galerkin (DG) method and an implicit backward differentiation formula of second order is used for temporal discretization. Chimera employed to realize a simple grid generation complex technical applications consisting multiple parts. Therefore, non-trivial overlapping areas could occur in numerical se...

This paper is concerned with the application of transient complete flux scheme to a radio frequency discharge model in one-dimensional geometry. The and exponential difference are used discretize plasma fluxes space. Temporal discretization performed by using implicit Euler method 2-step backward differentiation formula first second orders. Numerical experiments carried out evaluate order level...

I describe an adaptive h-reenement method for solving reaction-diiusion systems in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for irregular grids are used...

NO formation during ignition of combustible mixtures has been calculated in non– stationary two-dimensional systems by coupling the fluid flow and chemical reactions using “interactive flamelets”. The fluid flow was calculated by the PISO (Pressure– Implicit with Splitting of Operators) method to solve the Navier–Stokes equations. Further a convection–diffusion equation for the mixture fraction...

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equat...

Abstract. We derive optimal order, residual-based a posteriori error estimates for time discretizations by the two–step BDF method for linear parabolic equations. Appropriate reconstructions of the approximate solution play a key role in the analysis. To utilize the BDF method we employ one step by both the trapezoidal method or the backward Euler scheme. Our a posteriori error estimates are of...