Difference Scheme

A high resolution, explicit second order accurate, total variation diminishing (TVD) difference scheme using flux limiter approach for scalar hyperbolic conservation law and closely related convectively dominated diffusion problem is presented. Bounds and TVD region is given ...

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem−d2u(t)/dt2+Au(t)=g(t),(0≤t≤1),du(t)/dt−Au(t)=f(t),(−1≤t≤0),u(1)=u(−1)+μfor differential equations in a Hilbert spaceHwith a self-adjoint positive definite operatorAis considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented.

Abstaract. In this paper, we consider the problem of calculating the regime in a long multiwire line by a numerical method and the justification of the method for minimizing parasitic oscillations in the numerical solution of telegraph equations. A mathematical model of a multiwire electric line with distributed parameters with losses is given. Relations are obtained for the calculation of currents and voltages in the phase coordinate system. The justification of the numerical method for calculating the regime in such a line is giv-en, taking into account the mutual influence of the phases and the load of the line. For this, the method of the first differential approximation was used. A difference modified calculated scheme for telegraph equations in a diagonal form is constructed using Riemann invariants, with dissipative and dispersion terms in these rela-tions. This expression is called the first differential approximation and determines the order of approxima-tion of the dissipative and dispersion terms and the qualitative properties of the constructed difference scheme. Minimizing this expression will minimize the effects of dissipation and dispersion. The conditions for minimizing the dissipative and dispersion terms in the calculated numerical scheme and minimizing the error in the numerical solution are obtained. The results of the calculation of the wave process in the phase of an air multiwire line with a voltage of 110 kV are presented. Two weight parameters were introduced into the calculation program in such a way as to take into account the limiting states of the calculated scheme-dispersion and dissipation effects. For values that correspond to the condition for minimizing the dispersion effect, the input pulse propagates along the line without distortion, the damping is caused by the presence in the line of non-zero longitudinal resistance and the transverse active conductivity of the line. If the calcula-tions are performed with non-optimal values of the weight parameters, non-physical distortions appear at the wave front. The obtained results confirm the possibility of minimizing the dissipative and disperse effects of the numerical solution when using the proposed mathematical model of a multiwire line and the calculation scheme.

Аннотация. Приведена математическая модель многопроводной электрической линии с рас-пределенными параметрами, дано обоснование численного метода расчета в фазной системе коор-динат, разработана модифицированная расчетная схема, получены условия минимизации диссипа-тивных и дисперсионных членов и минимизации погрешности численного решения. Приведены ре-зультаты расчета волнового процесса в фазе воздушной многопроводной линии напряжением 110 кВ. Ключевые слова: математическая модель, разностная схема, инварианты Римана, первое дифференциальное приближение, минимизации диссипативных и дисперсионных членов. ного поля. Такие явления можно исследовать в фазной системе координат используя для описа-ния процессов в многопроводной линии систему дифференциальных уравнений в частных произ-водных [4-6], часто называемых телеграфными уравнениями. В случае длиной линии для получения ре-шения применяют численные методы [6-8], но в данном случае, в численном решении могут поя-виться осциляции, которые не являются отраже-нинем физической сущности процессов в линии [8-10]. В данной работе, рассматривается задача расчета режима в длинной многорповодной ли-нии численным методом и обоснование способа минимизации паразитных осциляций в числен-ном решении телеграфных уравнений.

We consider the abstract Cauchy problem for differential equation of the hyperbolic typev″(t)+Av(t)=f(t)(0≤t≤T),v(0)=v0,v′(0)=v′0in an arbitrary Hilbert spaceHwith the selfadjoint positive definite operatorA. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition on the three points for the numerical solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are established. In applications, the stability estimates for the solutions of the high order of accuracy difference schemes of the mixed-type boundary value problems for hyperbolic equations are obtained.

We present a fourth order compact finite difference scheme for a general three dimensionalconvection diffusion equation with variable coefficients on a uniform cubicgrid. This high order compact difference scheme is used to solve convection diffusionequation with boundary layers on a three dimensional nonuniform grid. We comparethe computed accuracy and computational efficiency of the fourth order compact differencescheme with that of

Intellectual property (IP) block reuse is essential for facilitating the design process of System-on-a-Chip. Sharing IP blocks in such a competitive market poses significant high security risks. IPs can be read, copied or even partitioned to cover the authorship proof. Creators and owners of IP designs want assurance that their content will not be illegally redistributed by consumers. Consumers, on the other hand, want assurance that the content they buy is legitimate. Digital watermarking, used with most of the shared digital media, has emerged as a candidate solution for helping copyright protection of IP blocks. In this paper, we outline IP watermarking and survey the current stateof -the-art of different schemes and algorithms. We also highlight the main technical problems that should be solved in order to let IP watermarking be used widely in industry.

In this paper a new efficient algorithm for computation of radio wave ray trajectories is described. The algorithm is based on an original second-order difference scheme with a specific "length-conservation" property, which allows to resolve the ray shape even in the regions where its curvature is high. Besides the scheme, the algorithm includes a number of mechanisms ensuring its correctness

The initial value problem for hyperbolic equationsd 2u(t)/dt 2+A u(t)=f(t)(0≤t≤1),u(0)=φ,u′(0)=ψ, in a Hilbert spaceHis considered. The first and second order accuracy difference schemes generated by the integer power ofAapproximately solving this initial value problem are presented. The stability estimates for the solution of these difference schemes are obtained.

Automated sleep staging based on EEG signal analysis provides an important quantitative tool to assist neurologists and sleep specialists in the diagnosis and monitoring of sleep disorders as well as evaluation of treatment efficacy. A complete visual inspection of the EEG recordings acquired during nocturnal polysomnography is time consuming, expensive, and often subjective. Therefore, feature extraction is implemented as an essential preprocessing step to achieve significant data reduction and to determine informative measures for automatic sleep staging. However, the analysis of the EEG signal and extraction of sensitive measures from it has been a challenging task due to the complexity and variability of this signal. We present three different schemes to extract features from the EEG signal: relative spectral band energy, harmonic parameters, and Itakura distance. Spectral estimation is performed by using autoregressive (AR) modeling. We then compare the performance of these sch...

In this paper asymptotic error expansions for mixed finite element approximations of the integro-differential equation are derived, and Richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation post-processing technique. The results of this paper provide new asymptotic expansions. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a-posteriori error estimators for this mixed finite element method. Finally, a numerical example is provided to validate the theoretical results.

ABSTRACT In many user interfaces with restricted input capabilities, a time-out is used to automatically change the user interface (UI) from one mode to another. In this paper, we study the learning of time-outs and the effect of feedback on it in the case of mobile phone text entry. The effects of three different feedback schemes (auditory/visual/no feedback) on the learning of two different time-out lengths were compared. We measured the response time (RT) from the time-out occurrence to the time of the user’s action. Error rates and the development of the RTs in different schemes were used as measures of learning. We also studied if the users learned to estimate the time-out lengths, or if they just reacted to the available feedback. There were three main findings. Without feedback, RTs had a great variation. Auditory feedback enabled faster RTs than visual feedback. Finally, we found evidence of short-term learning, but not much of a lasting effect. The possible application of adapting time-out length to user RT is discussed.

This paper is concerned with design and an integrated circuit implementation of multicarrier quadrature phase generators for application in analog spectral synthesis and orthogonal frequency division multiplexing transceiver using amplitude phase shift keying using 0.18µ technology. A ...

Bars with high and low filling factors serve the different schemes for beam transformation and fiber coupling. We report on highly efficient 8xx bars for operation in excess of 100 W and reliable broad-area single-emitter lasers (BASE) with 90 um aperture being capable to deliver in ...