Numerical Solution of Partial Differential Equations—III: Synspade 1975 provides information pertinent to those difficult problems in partial differential equations exhibiting some type of singular behavior. This book covers a variety of topics, including the mathematical models and their relation to experiment as well as the behavior of solutions of the partial differential equations involved. Organized into 16 chapters, this book begins with an overview of elastodynamic results for stress intensity factors of a bifurcating crack. This text then discusses the effects of nonlinearities, such as bifurcation, which occur in problems of nonlinear mechanics. Other chapters consider the equations of changing type and those with rapidly oscillating coefficients. This book discusses as well the effective computational methods for numerical solutions. The final chapter deals with the principal results on G-convergence, such as the convergence of the Green's operators for Dirichlet's and other boundary problems. This book is a valuable resource for engineers and mathematicians.

This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers.The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.

"Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.

Contemporary Developments in Continuum Mechanics and Partial Differential Equations

The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. The objective of the present work is to compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form.