KRYSI is a solver for stiff systems, and is a variant of an implicit Runge-Kutta solver called SIMPLE. Both KRYSI and SIMPLE use the same 3-stage third order SDIRK method. But where SIMPLE uses a direct (dense) solver for the associated linear systems, KRYSI uses a preconditioned Krylov method (preconditioned GMRES iteration). See  for details. The KRYSI solver is provided in separate single and double precision versions. Documentation on the usage of KRYSI is provided in the initial block of comment lines in the source file. An example program, with a sample output, is also supplied for each precision. ...  A. C. Hindmarsh and S. P. Norsett, ”KRYSI, An ODE Solver Combining a Semi-Implicit Runge-Kutta Method and a Preconditioned Krylov Method,” LLNL report UCID-21422, May 1988. (Also available as a PDF file.)
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References in zbMATH (referenced in 1 article )
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- Berzins, M.; Furzeland, R.M.: An adaptive theta method for the solution of stiff and nonstiff differential equations (1992)