is similar to uses LSODE LSODPK Livermore solver LSODKR http://identifiers.org/isbn/978-0444866073 LSODKR is an initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK [http://identifiers.org/biomodels.kisao/KISAO_0000093] and LSODE [http://identifiers.org/biomodels.kisao/KISAO_0000071] solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE [http://identifiers.org/biomodels.kisao/KISAO_0000071] are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration. Livermore solver for ordinary differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with root finding. Krylov subspace projection method