relaxation method


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relaxation method

[‚rē‚lak′sā·shən ‚meth·əd]
(mathematics)
A successive approximation method for solving systems of equations where the errors from an initial approximation are viewed as constraints to be minimized or relaxed within a toleration limit. Also known as relaxation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
According to the iterative format (4), we take time step h = 0.1 and use the Jacobi waveform relaxation method to solve the initial value problem (33).
Cadou, Numerical study of dynamic relaxation methods: Contribution to the modeling of inflatable lifejackets, LAP LAMBERT Academic Publishing Gmbh Co, Saarbrucken, Germany, 2012.
Caption: FIGURE 4: OCV estimated through the proposed method (in blue) over the OCV points obtained with the relaxation method (in red).
ZENNARO, The use of Runge-Kutta formulae in waveform relaxation methods, Appl.
Halpern, "Optimized Schwarz waveform relaxation methods for advection reaction diffusion problems," SIAM Journal on Numerical Analysis, vol.
In this paper, we have applied a spectral method called the multistage spectral relaxation method (MSRM) for the solutions of hyperchaotic complex systems.
[xi]\[DELTA][xi] 0.01 0.001 0.0005 0.0002 0.0001 Spectral relaxation method 0.1 0.07 0.22 0.43 0.95 1.93 0.3 0.13 0.65 1.38 3.18 6.01 0.5 0.20 1.14 2.26 5.48 10.69 0.7 0.27 1.72 3.14 7.70 15.08 0.9 0.35 2.30 4.25 10.05 19.57 Spectral qausilinearisation method 0.1 0.03 0.41 0.76 2.27 4.72 0.3 0.11 1.26 2.28 6.78 14.67 0.5 0.20 2.20 3.92 11.01 24.19 0.7 0.29 3.14 5.47 15.25 33.29 0.9 0.39 4.09 7.09 20.11 42.65 TABLE 4: Comparison between the SRM and Keller-Box approximate numerical values for f"(0, [xi]), g"(0, [xi]), [theta]'(0, [xi]), and [phi]'(0, [xi]) when [lambda] = 0.5, M = 2, c = 0.5, Sc = [gamma] = 1, and Pr = 1.5 in Example 2.
The Successive Relaxation Method has been used with great success to solve boundary problems; see, for example, [27-29].
The number of iterations differ, as that of the GMRES method has 5 iterations, whereas Conjugate Gradient method has 17 iterations as well, Successive-Over Relaxation method, has 15 iterations, while Gauss - Seidel has 17 iterations.
The minor fluctuation of the adapted relaxation method can be explained in Figure 4.
Randomized trials are needed to better define the role of various relaxation methods to safely improve psychological outcomes and enhance the quality of life among specific subgroups of coronary heart patients particularly older females and patients having external health locus of control or low level of self efficacy.
On the basis of the information developed using the compression stress relaxation method, ISO 3884(A), the design engineer is, however, still not able to create the right geometry for a static seal because all measurements are made at the temperature of the aging.