103,852 research outputs found
Theorema runge
No full textDi dalam pembahasan theorema RUnge diperlihatkan
bahwa suatu fungsi rasional di dalamisuatu daerah ter¬tentu dapat dapat didekati oleh suatu fungi analitik.
Mak& dapat dikatakan bahwa fungsi ra5ional akan konver-. gen ke suatu fungsi analitik atau limit dati fungsi ra-sional adalah fungsi analitik.
Salah satu kegunaan dari theorema Runge adalah di
pakai dalam pembuktian theorema Mittag-Leffler.
Maka akan dibahas sedikit tentang kegunaan theorema Runge t ers ebut.
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The Clinical Utility of Magnetic Resonance Imaging According to Field Strength, Specifically Addressing the Breadth of Current State-of-the-Art Systems, Which Include 0.55 T, 1.5 T, 3 T, and 7 T.
No full textABSTRACT
This review provides a balanced perspective regarding the clinical utility of magnetic resonance systems across the range of field strengths for which current state-of-the-art units exist (0.55 T, 1.5 T, 3 T, and 7 T). Guidance regarding this issue is critical to appropriate purchasing, usage, and further dissemination of this important imaging modality, both in the industrial world and in developing nations. The review serves to provide an important update, although to a large extent this information has never previously been openly presented. In that sense, it serves also as a position paper, with statements and recommendations as appropriate
Stability of Runge–Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])
No full textAbstractThis paper is concerned with the stability analysis of the Runge–Kutta methods for the equation u′(t)=au(t)+a0u([t]). The stability regions for the Runge–Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given
Mixed collocation methods for y” = f(x , y)
No full textThe second-order initial value problem y" = f(x,y), y(x(_0)) = y(_0), y'(x(_0)) = z(_0) which does not contain the first derivative explicitly and where the solution is oscillatory has been of great interest for many years. Our aim is to construct numerical methods which are tuned to act efficiently on strongly oscillating functions. The frequencies involved determine the oscillatory character of the function and as the frequencies approach zero, the classical methods are obtained. The exponential- fitting tool has become increasingly popular as it is specially tailored for oscillating functions. Many classes of methods have been used with exponential-fitting and this will be discussed in more detail in the thesis. Collocation methods are considered for which the basis functions are combinations of polynomial and trigonometric terms. The resulting methods can be regarded as Runge-Kutta-Nyström methods with steplength dependent coefficients. We show how order conditions may be obtained, investigate the stability and other properties of particular methods and present some numerical results
Effective simulation techniques for biological systems
No full textIn this paper we give an overview of some very recent work on the stochastic simulation of systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the Balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and discuss how novel computing implementations can enhance the performance of these simulations
Preservation of oscillations of the Runge–Kutta method for equation x′(t)+ax(t)+a1x([t−1])=0
No full textAbstractThe paper deals with the preservation of oscillations of the Runge–Kutta method for equation x′(t)+ax(t)+a1x([t−1])=0. It is proved that oscillations of the analytic solution are preserved by the Runge–Kutta method. Special interpolation functions of the numerical solutions are given. It turns out that zeros of the interpolation function of the numerical solution converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge–Kutta method. Some numerical experiments are presented
Johanna Runge?
No full textPhotograph shows a waist-length portrait of young woman, possibly Johanna Runge
Patankar-Type Runge-Kutta Schemes for Linear PDEs
No full textWe study the local discretization error of Patankar-type Runge-Kutta methods
applied to semi-discrete PDEs. For a known two-stage Patankar-type scheme the
local error in PDE sense for linear advection or diffusion is shown to be of
the maximal order for sufficiently smooth and positive
exact solutions. However, in a test case mimicking a wetting-drying situation
as in the context of shallow-water flows, this scheme yields large errors in
the drying region. A more realistic approximation is obtained by a modification
of the Patankar approach incorporating an explicit testing stage into the
implicit trapezoidal rule
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