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Numerical solution of initial-value problems in differential-algebraic equations
The DAE home page introduces theoretical advances Numerical analysis advancements DAE software DASSL Supplementary bibliography Index.
Computer methods for ordinary differential equations and differential-algebraic equations
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.
A description of dassl: a differential/algebraic system solver
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.
Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations
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.
Efficient step size selection for the tau-leaping simulation method.
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.
The slow-scale stochastic simulation algorithm.
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.
Efficient formulation of the stochastic simulation algorithm for chemically reacting systems.
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.
A New Look at Proper Orthogonal Decomposition
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.
Differential-algebraic equations
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.
Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems
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