Numerische Behandlung von Differentialgleichungen ist seit vielen Jahren mit einiger RegelmaBigkeit Thema einer Tagung am Mathematischen For schungsinstitut in Oberwolfach gewesen. Wie bei den frilheren Tagungen wurde auch diesmal ilber in neuerer Zeit erzielte Fortschritte bei sehr ver schiedenartigen numerischen Methoden berichtet. Neben dem allgemeinen Uberblick fand bei dieser Tagung das Gebiet der freien Randwertaufgaben besondere Berilcksichtigung. Solche Probleme bei partiellen Differentialglei chungen galten noch vor etwa 5 Jahren als ein auBerordentlich schwieriges, numerisch kaum...

Dieser Band bringt Manuskripte zu Vortragen einer Tagung, die in Oberwolfach vom 3. 6. bis 9. 6. 1973 unter Leitung der Unterzeichner veranstaltet wurde. Die letzte Tagung uber numerische Probleme der Approximationstheorie in Oberwolfach fand 1971 statt. Daher hatte die jetzige Veranstaltung das Ziel, den in der Zwischenzeit erreichten Fortschritt auf diesem Gebiet durch ausgewahlte V ortrage erkennen zu lassen. Die grosse Zahl der Vortrage sowie die Fulle der behandelten Themen zeigte die wachsende Bedeutung, die diesem Gebiet auch in der Zukunft fur die Anwendungen zukommt und macht...

The analysis of parameter-dependent nonlinear has received much attention in recent years. Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity theory. These theories contribute to the understanding of many nonlinear phenomena in nature and they form the basis for various analytical and numerical tools, which provide qualitative and quantitative results about nonlinear systems. In...

The past 20 years have shown a rapid growth in the theoretical understanding, useful applications and widespread acceptance of multigrid in the applied sciences, and new tasks continue to arise that are better addressed from a special multigrid point of view. These developments have served to make multigrid one of the key techniques in modern computing methods. Most prominent among the new issues are parallel computing and adaptive computations. Multigrid methods also have considerable impact on computational fluid dynamics. This influence is reflected in the present, carefully screened...

Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation...

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. This book aims to present in detail the original proof for Gromov's compactness theorum for pseudo-holomorphic curves. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities. A special chapter is devoted to relevant features of hyperbolic surfaces, where thick-thin decomposition is described. This text should be accessible to...