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. Sherratt, Jonathan A.: How does nonlocal dispersal affect the selection and stability of periodic traveling waves? (2018)
  2. Tranquilli, Paul; Glandon, S. Ross; Sarshar, Arash; Sandu, Adrian: Analytical Jacobian-vector products for the matrix-free time integration of partial differential equations (2017)
  3. 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)
  4. 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)
  5. Sherratt, Jonathan A.: Invasion generates periodic traveling waves (wavetrains) in predator-prey models with nonlocal dispersal (2016)
  6. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  7. 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)
  8. Zhang, Hong; Sandu, Adrian; Tranquilli, Paul: Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods (2015)
  9. 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)
  10. 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)
  11. 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)
  12. Tranquilli, Paul; Sandu, Adrian: Exponential-Krylov methods for ordinary differential equations (2014)
  13. Hillen, Thomas; Painter, Kevin J.: Transport and anisotropic diffusion models for movement in oriented habitats (2013)
  14. Beck, Steffen; Weiner, Rüdiger; Podhaisky, Helmut; Schmitt, Bernhard A.: Implicit peer methods for large stiff ODE systems (2012)
  15. Rashkov, Peter; Schmitt, Bernhard A.; Søgaard-Andersen, Lotte; Lenz, Peter; Dahlke, Stephan: A model of oscillatory protein dynamics in bacteria (2012)
  16. Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P.; Chaplain, Mark A. J.: Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation (2011)
  17. Bloomfield, J. M.; Painter, K. J.; Sherratt, J. A.: How does cellular contact affect differentiation mediated pattern formation? (2011)
  18. Daniel, Gregory B.; Cavalca, Katia L.: Analysis of the dynamics of a slider-crank mechanism with hydrodynamic lubrication in the connecting rod-slider joint clearance (2011)
  19. Painter, Kevin J.; Hillen, Thomas: Spatio-temporal chaos in a chemotaxis model (2011)
  20. Xue, Chuan; Hwang, Hyung Ju; Painter, Kevin J.; Erban, Radek: Travelling waves in hyperbolic chemotaxis equations (2011)

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