The purpose of the present paper is to study theoretically the stability and accuracy of dualtime-steppingmethods for the advection-diffusionequation, in conjuctionwith high-order upwindbiased space-discretizations, and high-order backward-differences time-discretizations. These results are in particular analyzed for typical nondimensional time-steps encountered in the simulation of wall-bounde...

We present a new short-term tracking algorithm called Best Displacement Flow (BDF). This approach is based on the idea of ‘Flock of Trackers’ with two main contributions. The first contribution is the adoption of an efficient clustering approach to identify what we term the ‘Best Displacement’ vector, used to update the object’s bounding box. This clustering procedure is more robust than the me...

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...

An (α, β, γ)-LSBS RSA denotes an RSA system with primes sharing α least significant bits, private exponent d with β least significant bits leaked, and public exponent e with bit-length γ. Steinfeld and Zheng showed that LSBS-RSA with small e is inherently resistant to the BDF attack, but LSBS-RSA with large e is more vulnerable than standard RSA. In this paper, we improve the BDF attack on LSBS...

We analyze the discretization of the periodic initial value problem for Kuramoto–Sivashinsky type equations with Burgers nonlinearity by implicit– explicit backward difference formula (BDF) methods, establish stability and derive optimal order error estimates. We also study discretization in space by spectral methods.

We have developed a structured adaptive mesh refinement (SAMR) method for parabolic partial differential equation (PDE) systems. Solutions are calculated using the finite-difference or finite-volume method in space and backward differentiation formula (BDF) integration in time. The combination of SAMR in space and BDF in time is designed for problems where the fine-scale profile of sharp fronts...

We propose a method for solving a model of age-dependent population diffusion with random dispersal. This method, unlike previous methods, allows for variable time steps and independent age and time discretizations. We use a moving age discretization that transforms the problem to a coupled system of parabolic equations. The system is then solved by backward differences in time and a Galerkin a...

granular media of CoCrPtTa structure (type a) and micromagnetic standard problem #4 has been done. Moreover, an investigation of the effect of the maximum dimension of the Krylov subspace projection methods, within the Ordinary Differential Equations (ODEs) context, on the speed of micromagnetic simulations on granular media of Co structure (type b) has been done. The stiffness of the problems ...

One-Leg Multistep (OLM) methods for initial value problems in ODEs use a nonlinear multistep formula to compute the solution at the next integration point. This paper shows that there exists an evaluation point t∗ which gives an OLM formula more precise than BDF’s and (almost) precisely A(α)-stable for a k-step method (k ≤ 6), and whose stability angle is essentially similar to BDF’s. The stabi...

CVODE is a package written in C for solving initial value problems for ordinary di erential equations. It provides the capabilities of two older Fortran packages, VODE and VODPK. CVODE solves both sti and nonsti systems, using variable-coe cient Adams and BDF methods. In the sti case, options for treating the Jacobian of the system include dense and band matrix solvers, and a preconditioned Kry...