pde2path

pde2path - a Matlab package for continuation and bifurcation in 2D elliptic systems. pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetool, and is explained by a number of examples, including Bratu’s problem, the Schnakenberg model, Rayleigh Benard convection, and von Karman plate equations. These serve as templates to study new problems. The basic algorithm is a one parameter arclength-continuation, including a parallel computing version. Stability calculations, error control and mesh-handling, and some elementary time-integration are also supported. The continuation, branch-switching, plotting etc are performed via matlab command-line function calls guided by the Auto style.


References in zbMATH (referenced in 21 articles , 1 standard article )

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  1. Hao, Wenrui; Xue, Chuan: Spatial pattern formation in reaction-diffusion models: a computational approach (2020)
  2. Lappicy, Phillipo: A symmetry property for fully nonlinear elliptic equations on the sphere (2020)
  3. Tzou, J. C.; Tzou, L.: Spot patterns of the Schnakenberg reaction-diffusion system on a curved torus (2020)
  4. Chirilus-Bruckner, M.; van Heijster, P.; Ikeda, H.; Rademacher, J. D. M.: Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system (2019)
  5. de Witt, Hannes: Beyond all order asymptotics for homoclinic snaking in a Schnakenberg system (2019)
  6. Lloyd, David J. B.: Invasion fronts outside the homoclinic snaking region in the planar Swift-Hohenberg equation (2019)
  7. Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.: Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system (2019)
  8. Gavish, Nir: Poisson-Nernst-Planck equations with steric effects -- non-convexity and multiple stationary solutions (2018)
  9. Lin, T.-S.; Tseluiko, D.; Blyth, M. G.; Kalliadasis, S.: Continuation methods for time-periodic travelling-wave solutions to evolution equations (2018)
  10. Barbieri, Ettore; Ongaro, Federica; Pugno, Nicola Maria: A (J)-\textitintegral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami (2017)
  11. Grass, Dieter; Uecker, Hannes: Optimal management and spatial patterns in a distributed shallow lake model (2017)
  12. Jüngel, Ansgar; Kuehn, Christian; Trussardi, Lara: A meeting point of entropy and bifurcations in cross-diffusion herding (2017)
  13. Dohnal, Tomáš; Uecker, Hannes: Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation (2016)
  14. Marojević, Želimir; Göklü, Ertan; Lämmerzahl, Claus: ATUS-PRO: a FEM-based solver for the time-dependent and stationary Gross-Pitaevskii equation (2016)
  15. Wetzel, Daniel: Pattern analysis in a benthic bacteria-nutrient system (2016)
  16. Kuehn, Christian: Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs (2015)
  17. Siero, E.; Doelman, A.; Eppinga, M. B.; Rademacher, J. D. M.; Rietkerk, M.; Siteur, K.: Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes (2015)
  18. Zhelyazov, D.; Han-Kwan, D.; Rademacher, J. D. M.: Global stability and local bifurcations in a two-fluid model for tokamak plasma (2015)
  19. Laing, Carlo R.: Numerical bifurcation theory for high-dimensional neural models (2014)
  20. Uecker, Hannes; Wetzel, Daniel: Numerical results for snaking of patterns over patterns in some 2D Selkov-Schnakenberg reaction-diffusion systems (2014)

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