Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure

Most methods for solving stLff systems are based on implicit formulas and require the use of Newtonlike iterations. The cost of the matrLx operations in the iteration scheme of these methods can be quite high. A new iteration scheme is developed which exploits the structure of the system and also allows fast updating of the iteration matrix after a stepsize or order change. The technique is particularly useful when the stiffness is due to only a few components of a large system, and is applicable to most methods for stiff systems. It is based on an automatic partitioning of the system into subsystems corresponding to stiff and nonstiff parts. This partitioning is then exploited in the solution of the system of equations that must be solved on each time step.

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