By E. L. Allgower, C.-S. Chien, K. Georg (auth.), Hans D. Mittelmann, Dirk Roose (eds.)
The research of parameter-dependent nonlinear has obtained a lot realization lately. Numerical continuation innovations let the effective computation of resolution 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, according to bifurcation conception and singularity thought. those theories give a contribution to the knowledge of many nonlinear phenomena in nature they usually shape the root for numerous analytical and numerical instruments, which supply qualitative and quantitative effects approximately nonlinear platforms. during this factor we've gathered a few papers facing continuation thoughts and bifurcation difficulties. Readers acquainted with the notions of continuation and bifurcation will locate contemporary study effects addressing various elements during this factor. those that intend to benefit in regards to the box or a selected subject in it can locate it priceless to first seek advice previous literature at the numerical remedy of those difficulties including a few theoretical historical past. The papers during this factor fall certainly into various groups.
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Additional info for Continuation Techniques and Bifurcation Problems
Sci. 9 (1987) 240-250. [14) E. D. Mittelmann, Extension of Beckert's continuation method to variational inequalities, Math. , submitted. [15) E. D. Mittelmann, On the continuation for variational inequalities depending on an eigenvalue parameter, Math. Meth. Appl. Sci. 11 (1988) 95-104. D. Mittelmann, An efficient algorithm for bifurcation problems of variational inequalities, Math. Compo 41 (1983) 473-485. D. Mittelmann, On continuation for variational inequalities, SIAM J. Numer. Anal. 24 (1987) 1374-138l.
D. Mittelmann, Approximation of obstacle problems by continuation methods, SIAM J. Numer. Anal. 2S (1988) 1409-143l. [3) 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. W. B. Keller, Path following near bifurcation. Comm. Pure Appl. Math. 34 (1981) 149-175. [5) W. D. Mittelmann, On multi-grid methods for variational inequalities, Numer. Math. 42 (1983) 65-76. W.
E o II Uo ( oJi») + KSuo ( oJj)) II = oJi+ 1). where the pair (U o, ~o) with uJu o + ~20 = 1 has to be computed only for the very first continuation step while in the sequel it may be obtained by means of u o( oJj) - u o( oJi- l» and Ao( oJi» - Ao( oJi- l», respectively. oh; ifk=Othen (Uk(O~), Ak(O~»:= Ek(uk(od, Ak(Ok» else begin array Uk -1; Uk(O~):= min(uk(ok) + pLl(Uk-l(O~) - Uk-l(Ok», o/k); Ak(O~):= Ak(Ok) + Ak-l(O~) - Ak-l(Ok); for i:= 1 step 1 until 'Tk do MGCVI (k, Uk' Ak> if k = 1 go to end NMGCVI else 0k:= (J~~ gk); for j:= 0 step 1 unril k do NMGCVI (j, ui ' Ai' g); end NMGCVI.
Continuation Techniques and Bifurcation Problems by E. L. Allgower, C.-S. Chien, K. Georg (auth.), Hans D. Mittelmann, Dirk Roose (eds.)