The intent of this tutorial is to discuss hsolve, the implicit equation solver of GENESIS. First some of the equations important to neuro-biological modeling will be discussed. We illustrate how GENESIS handles them numerically by inspection of the C code and the simulation schedule. Afterwards the focus will be on implicit solution with hsolve. We discuss a number of internal secrets of hsolve that explain how it gets its extra performance : examples of channel and table rearrangements, updated simulation schedule, internal data streams, interoperability with synchans via discrete events. Furthermore the use of findsolvefield is discussed and interactions with external objects are highlighted.
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