ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs. We present a Krylov-W-code ROWMAP for the integration of stiff initial value problems. It is based on the ROW-methods of the code ROS4 of Hairer and Wanner and uses Krylov techniques for the solution of linear systems. A special multiple Arnoldi process ensures order p = 4 already for fairly low dimensions of the Krylov subspaces independently of the dimension of the differential equations. Numerical tests and comparisons with the multistep code VODPK illustrate the efficiency of ROWMAP for large stiff systems. Furthermore, the application to nonautonomous systems is discussed in more detail.

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  1. Villa, Chiara; Gerisch, Alf; Chaplain, Mark A. J.: A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis (2022)
  2. Klinge, Marcel; Hernández-Abreu, D.; Weiner, R.: A comparison of one-step and two-step W-methods and peer methods with approximate matrix factorization (2021)
  3. Buttenschön, Andreas; Liu, Yue; Edelstein-Keshet, Leah: Cell size, mechanical tension, and GTPase signaling in the single cell (2020)
  4. Herath, Samantha; Lobo, Daniel: Cross-inhibition of Turing patterns explains the self-organized regulatory mechanism of planarian fission (2020)
  5. Hillen, Thomas; Buttenschön, Andreas: Nonlocal adhesion models for microorganisms on bounded domains (2020)
  6. Sherratt, Jonathan A.: How does nonlocal dispersal affect the selection and stability of periodic traveling waves? (2018)
  7. Tranquilli, Paul; Glandon, S. Ross; Sarshar, Arash; Sandu, Adrian: Analytical Jacobian-vector products for the matrix-free time integration of partial differential equations (2017)
  8. Blom, David S.; Birken, Philipp; Bijl, Hester; Kessels, Fleur; Meister, Andreas; van Zuijlen, Alexander H.: A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows (2016)
  9. González-Pinto, S.; Hernández-Abreu, D.; Pérez-Rodríguez, S.; Weiner, R.: A family of three-stage third order AMF-W-methods for the time integration of advection diffusion reaction PDEs. (2016)
  10. Sherratt, Jonathan A.: Invasion generates periodic traveling waves (wavetrains) in predator-prey models with nonlocal dispersal (2016)
  11. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  12. Carlier, Aurélie; Geris, Liesbet; van Gastel, Nick; Carmeliet, Geert; Van Oosterwyck, Hans: Oxygen as a critical determinant of bone fracture healing -- A multiscale model (2015)
  13. Zhang, Hong; Sandu, Adrian; Tranquilli, Paul: Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods (2015)
  14. Beck, S.; González-Pinto, S.; Pérez-Rodríguez, S.; Weiner, R.: A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems (2014)
  15. Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J.: Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns (2014)
  16. Rashkov, Peter; Schmitt, Bernhard A.; Keilberg, Daniela; Søgaard-Andersen, Lotte; Dahlke, Stephan: A model for spatio-temporal dynamics in a regulatory network for cell polarity (2014)
  17. Tranquilli, Paul; Sandu, Adrian: Exponential-Krylov methods for ordinary differential equations (2014)
  18. Hillen, Thomas; Painter, Kevin J.: Transport and anisotropic diffusion models for movement in oriented habitats (2013)
  19. Beck, Steffen; Weiner, Rüdiger; Podhaisky, Helmut; Schmitt, Bernhard A.: Implicit peer methods for large stiff ODE systems (2012)
  20. Rashkov, Peter; Schmitt, Bernhard A.; Søgaard-Andersen, Lotte; Lenz, Peter; Dahlke, Stephan: A model of oscillatory protein dynamics in bacteria (2012)

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