An efficient iterative algorithm is applied to seek analytical solutions of higher dimensional initial boundary value problems (IBVPS) with variable coefficients. The proposed scheme finds the solution without any discretization, perturbation, transformation or restrictive assumptions and avoids the round off errors. Numerical results clearly reveal the complete reliability and efficiency of th...

In this paper, a finite difference method for initial-boundary value problem of nonlinear Regularized-Long-Wave equation was considered. A energy conservative finite difference scheme of three levels was proposed, convergence and stability of difference solution was proved, if picking suitably,the accuracy of the new scheme is higher than others, so the method is efficient and reliable.

A linear-implicit finite difference scheme is given for the initial-boundary problem of GBBMBurgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is effici...

We present a case study examining the creation of an efficient preconditioner for solution of incompressible flow problems. We trace algorithm development from theoretical considerations, through initial implementation and testing, to parallel performance for large−scale systems. We demonstrate that early coupling of the development process with existing code can reduce debugging time and ease ...

What happens if the Xi ’s take values in a (real) Banach space (B, ‖ · ‖)? In such cases, in particular when the square of the norm ‖ · ‖ is not given by an inner product, we are aiming at inequalities of the following type: Let X1, X2, . . . , Xn be independent random vectors with values in (B, ‖ · ‖) with EXi = 0 and E‖Xi‖2 < ∞. With Sn := ∑n i=1 Xi we want to show that E‖Sn‖ ≤ K n ∑ i=1 E‖Xi...

In important papers on cake-cutting – one of the key areas in fair division and resource allocation – the measuretheoretical fundamentals are not fully correctly given. It is not clear (i) which family of sets should be taken for the pieces of cake, (ii) which set-functions should be used for evaluating the pieces, and (iii) which is the relationship between various continuity properties appear...

Abst rac t . We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have reached our goals. We also discuss some recent theoretical developments. This paper contains no new technical material. It is intended as a guide to existing publications about the system. We ref...

This paper presents a novel method to compensate the eeects of exi-bility in belt-driven drive trains. Such drives are found in robot manipulators, for example, where drive exibility is undesirable. Unfortunately, the eeects of exibility can be diicult to compensate using the primary actuator, due to bandwidth limitations. By introducing a second actuator, which applies a force to the belt at a...

Statistical approaches to study the properties of neurons in sensory system ascribe the selectivity of neurons in visual and auditory cortices to regularities of signals in natural environment. “Efficient coding” hypothesis is an outstanding theory that explains the work of sensory system in discarding unnecessary data and supplying higher order brain areas with the most informative features in...