By E. L. Allgower, C.-S. Chien, K. Georg (auth.), Hans D. Mittelmann, Dirk Roose (eds.)
The research of parameter-dependent nonlinear has acquired a lot recognition in recent times. Numerical continuation ideas permit the effective computation of answer branches in a one-parameter challenge. in lots of situations continuation tactics are used as a part of a extra whole research of a nonlinear challenge, in keeping with bifurcation thought and singularity concept. those theories give a contribution to the certainty of many nonlinear phenomena in nature they usually shape the root for varied analytical and numerical instruments, which supply qualitative and quantitative effects approximately nonlinear platforms. during this factor we have now gathered a couple of papers facing continuation innovations and bifurcation difficulties. Readers conversant in the notions of continuation and bifurcation will locate fresh examine effects addressing numerous points during this factor. those that intend to benefit in regards to the box or a particular subject in it could locate it beneficial to first seek advice past literature at the numerical remedy of those difficulties including a few theoretical history. The papers during this factor fall certainly into diverse groups.
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95 for I = 4 thus reflecting the expected asymptotic convergence rate 0(1 - h~) for that single-grid iteration scheme. Finally, for comparison with different (single-grid) continuation strategies applied to the same problem the reader is referred to  and . =! 25 (b) 20 -- 20 25 30 15 < <: I 10 0~2~~~~~~~---C~~'7----~--C---~1"0~~11~--'12--~13 L~r1BOA Fig. 2. 0. 0. 0. H. D. Mittelmann / Multi-grid continuation strategy 45 20 IS 10 OT2~~~~~~~~-C~-C~~8C-~C-~~IOC-~I'I~~12~~1'3~~14 LRHBOR Fig.
Cryer, Multi-grid algorithms for the solution of linear complementarity problems arising from free boundary problems, SIAM J. Sci. Stat. Comput. 4 (1983) 655-684.  F. Conrad, F. -M. Brauner and B. Nicolaenko, Nonlinear eigenvalue problems in elliptic variational inequalities: A local study, Comm. Partial Differential Equations 10 (1985) 151-190.  R. L. Lions and R. Tremolieres, Numerical Analysis of Variational Inequalities (North-Holland, Amsterdam, 1981).  W. Hackbusch, Multi-grid solution of continuation problems, in: R.
The first limit point on the curve is the trigger point while the second one is the holding point. The response curve and its limit points have physical interpretations . We will now discuss some specific examples, but refer the reader to  for a number of additional examples. 1. Trigger-point computations Figure 3 shows the result of a trigger simulation using continuation for a twin-tub CMOS cross-section like that in Fig. 1. The external voltage was applied to the p+ source/drain (see Fig.