ODEPACK, a systematized collection of ODE solvers. ODEPACK is a collection of Fortran solvers for the initial value problem for ordinary differential equation systems. It consists of nine solvers, namely a basic solver called LSODE and eight variants of it -- LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS. The collection is suitable for both stiff and nonstiff systems. It includes solvers for systems given in explicit form, dy/dt = f(t,y), and also solvers for systems given in linearly implicit form, A(t,y) dy/dt = g(t,y). Two of the solvers use general sparse matrix solvers for the linear systems that arise. Two others use iterative (preconditioned Krylov) methods instead of direct methods for these linear systems. The most recent addition is LSODIS, which solves implicit problems with general sparse treatment of all matrices involved.

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  8. Ong, Benjamin W.; Haynes, Ronald D.; Ladd, Kyle: Algorithm 965: RIDC methods: a family of parallel time integrators (2016)
  9. Andersson, C., Führer, C., Åkesson, J.: Assimulo: A unified framework for ODE solvers (2015)
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  13. Kotov, Dmitry V.; Yee, H.C.; Panesi, Marco; Prabhu, Dinesh K.; Wray, Alan A.: Computational challenges for simulations related to the NASA electric arc shock tube (EAST) experiments (2014)
  14. Novikov, Eugeny A.; Novikov, Anton E.: Variable structure algorithm using explicit and $L$-stable methods (2014)
  15. Schiller, Ulf D.: A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method (2014)
  16. Fischer, Cyril: Massive parallel implementation of ODE solvers. (2013)
  17. Strohmaier, Alexander; Uski, Ville: An algorithm for the computation of eigenvalues, spectral zeta functions and zeta-determinants on hyperbolic surfaces (2013)
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