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.

References in zbMATH (referenced in 151 articles )

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  1. Batra, R. C.; Zhu, Z. G.: Effect of loading direction and initial imperfections on the development of dynamic shear bands in a FCC single crystal (1995)
  2. Carr, J.; Duncan, D. B.; Walshaw, C. H.: Numerical approximation of a metastable system (1995)
  3. Diamantakis, M. T.: The NUMOL solution of time-dependent PDEs using DESI Runge-Kutta formulae (1995)
  4. Franco, J. M.: An explicit hybrid method of Numerov type for second-order periodic initial-value problems (1995)
  5. Jorquera, Héctor: Simple algorithm for solving linear integrodifferential equations with variable limits (1995)
  6. Knoth, Oswald; Wolke, Ralf: Numerical methods for the solution of large kinetic systems (1995)
  7. Burrage, K.; Pohl, B.: Implementing an ODE code on distributed memory computers (1994)
  8. Moore, Peter K.; Petzold, Linda R.: A stepsize control strategy for stiff systems of ordinary differential equations (1994)
  9. Sun, Pu; Chock, David P.; Winkler, Sandra L.: An implicit-explicit hybrid solver for a system of stiff kinetic equations (1994)
  10. Wang, Y. M.; Batra, R. C.: Effect of kinematic hardening on the initiation and growth of shear bands in plane strain deformations of a thermoviscoplastic solid (1994)
  11. Weisbuch, Gérard; Oprea, Mihaela: Capacity of a model immune network (1994)
  12. Abdallah, Haïscam; Marie, Raymond: The uniformized power method for transient solutions of Markov processes (1993)
  13. Andrzejewski, Thomas; Bock, Hans Georg; Eich, Edda; von Schwerin, Reinhold: Recent advances in the numerical integration of multibody systems (1993)
  14. Brugnano, L.; Trigiante, D.: A parallel preconditioning technique for boundary value methods (1993)
  15. Denk, G.: A new numerical method for the integration of highly oscillatory second- order ordinary differential equations (1993)
  16. Grantham, Walter J.; Lee, Byoungsoo: A chaotic limit cycle paradox (1993)
  17. Batra, R. C.; Ko, K.-I.: An adaptive mesh refinement technique for the analysis of shear bands in plane strain compression of a thermoviscoplastic solid (1992)
  18. Carter, Richard G.: On the global convergence of trust region algorithms using inexact gradient information (1991)
  19. Sugiura, Hiroshi; Torii, Tatsuo: A method for constructing generalized Runge-Kutta methods (1991)
  20. Augenbaum, J. M.: An adaptive pseudospectral method for discontinuous problems (1989)

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