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LSODE
LSODPK
2008-07-08
http://identifiers.org/isbn/978-0444866073
LSODPK is a set of FORTRAN subroutines for solving the initial value problem for stiff and nonstiff systems of ordinary differential equations. In solving stiff systems, LSODPK uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods [http://identifiers.org/biomodels.kisao/KISAO_0000354]. The user must select the desired Krylov method and supply a pair of routine to evaluate, preprocess, and solve the (left and/or right) preconditioner matrices. Aside from preconditioning, the implementation is matrix-free, meaning that explicit storage of the Jacobian (or related) matrix is not required. The method is experimental because the scope of problems for which it is effective is not well-known, and users are forewarned that LSODPK may or may not be competitive with traditional methods on a given problem. LSODPK also includes an option for a user-supplied linear system solver to be used without Krylov iteration.
Livermore solver for ordinary differential equations for stiff and nonstiff systems with krylov corrector iteration
NLN
Livermore solver
Krylov subspace projection method