This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications.Expand

The algorithms and strategies used in DASSL, for the numerical solution of implicit systems of differential/algebraic equations, are outlined, and some of the features of the code are explained.Expand

Test results indicate that many problems can be solved more efficiently using this scheme than with a single class of methods, and that the overhead of choosing the most efficient methods is relatively small.Expand

An improved procedure for estimating the largest value for tau that is consistent with theory and more accurate, easier to code, and faster to execute than the currently used procedure is presented.Expand

A systematic approximate theory is developed that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events, and when those challenges can be overcome, very substantial increases in simulation speed can be realized.Expand

It is concluded that for most practical problems the optimized direct method is the most efficient formulation of SSA, in contrast to the widely held belief that Gibson and Bruck's next reaction method.Expand

Some basic properties of the proper orthogonal decomposition (POD) method as it is applied to data compression and model reduction of finite dimensional nonlinear systems are investigated and why in some applications this sensitivity is a concern while in others it is not.Expand

The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.Expand

In this paper, a new algorithm for the solution of large-scale systems of differential-algebraic equations is described. It is based on the integration methods in the solver DASSL, but instead of a… Expand