Local and global errors are now computed for selected unknowns. Since step doubling is used for this purpose, the new feature is computationally intensive and should be used with care. So is another new feature: curve labels. The location of these labels is estimated so, for graphs with many curves and/or plotting points, turning labels on is recommended once a problem has been solved, not during solution. The third most significant change is the addition of curve previews to solvers, making it easier to create graphs.
Lots of minor improvements and bug fixes. Some functions, the hyperbolic ones for example, were not computed correctly in the previous release. This release has been created using OS X 10.9.4 but still supports earlier versions.
Changes aimed at improving performance and stability and at reducing both memory and CPU usage have resulted in a 20% increase in performance, which should be more noticeable in larger problems. A more reliable algorithm for initiation and a new algorithm for branch switching at simple bifurcation points are now available in continuation problems. In addition, many bugs haven been fixed in the new user interface for problem definition.
No changes in any of the numerical algorithms, all changes in this version are interface related. There is a new user interface for problem definition. Natural language can be used to specify a problem, for example solve y = cos(y). In this new interface, graphs are automatically generated. For experienced users who prefer the original user interface, that interface is still available.
Autoscaling is now the default behavior of graphs but can be disabled whenever axis properties are modified. Clicking on a graph component, an axis for example, or a title, or a curve, brings up the corresponding editor.
Curves, points, and links now have the ability to switch solvers automatically. This can be a convenient feature during problem development, when different solvers are being tested until the right solver is found.
Mac OS X 10.6.8 is supported again. The most significant change is the addition of continuation along branches of stationary solutions. New example scripts have been created to illustrate this feature. DAE Solver will perform linear stability analysis and it will search for turning points, simple bifurcation points, and Hopf bifurcation points. Performance has improved too, with larger problems being almost twice as fast as in the previous version.
OS X Lion is required. Key runtime behaviors supported: automatic termination, automatic data-saving, and interface preservation. Also new is simple animation in graphs and the ability to save an animation as a movie file. Curves in a graph are no longer constrained to sharing the same horizontal axis variable. Number of function evaluations and number of jacobian evaluations are now reported.
Most visible change is the addition of an interface for creating, editing, removing, importing, and exporting integration methods. Users are no longer constrained to the methods provided as factory settings. The most important change is however an invisible one. The algorithms used in solving equations are more robust in this version than in the previous one. Special attention has been paid to higher index problems, as illustrated by the new examples.
Minor additional changes include context sensitive help, better diagnostics when solution fails, migration to 64-bit architecture, higher number of nonlinear iterations allowed, and the usual list of bug fixes. Of these bugs, the most serious one was in the parsing order of products and divisions, right-to-left in Version 1.0 becomes left-to-right in Version 1.1.
DAE Solver is not a substitute for professional tools that accomplish the same purpose but may be more powerful, and are often more expensive. The main motivation in developing this tool was to provide an environment that is as easy to learn and to use as possible. On your first attempt at using DAE Solver, you should be able to set up a problem and to generate results that can be moved to your application of choice.
Even with all the tools available for application development, it has been time consuming to bring this application to its current state. A significant percentage of that time was spent on making sure that DAE Solver would follow the Apple Human Interface Guidelines. The algorithms used in solving equations were not neglected, but there is still room for improvement. Work on the next version has concentrated on making those algorithms faster and more robust.