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 44 articles , 1 standard article )

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  1. Boullé, Nicolas; Farrell, Patrick E.; Paganini, Alberto: Control of bifurcation structures using shape optimization (2022)
  2. Mandel, Rainer; Moitier, Zoïs; Verfürth, Barbara: Nonlinear Helmholtz equations with sign-changing diffusion coefficient (2022)
  3. Uecker, Hannes: Continuation and bifurcation in nonlinear PDEs - algorithms, applications, and experiments (2022)
  4. Breden, Maxime; Kuehn, Christian; Soresina, Cinzia: On the influence of cross-diffusion in pattern formation (2021)
  5. Carter, Paul; Rademacher, Jens D. M.; Sandstede, Björn: Pulse replication and accumulation of eigenvalues (2021)
  6. Ehstand, Noémie; Kuehn, Christian; Soresina, Cinzia: Numerical continuation for fractional PDEs: sharp teeth and bloated snakes (2021)
  7. Gavish, Nir; Kenneth, Oded; Keren, Amit: Ginzburg-Landau model of a stiffnessometer -- a superconducting stiffness meter device (2021)
  8. Morita, Yoshihisa; Seirin-Lee, Sungrim: Long time behavior and stable patterns in high-dimensional polarity models of asymmetric cell division (2021)
  9. Sánchez Umbría, J.; Net, M.: Continuation of double Hopf points in thermal convection of rotating fluid spheres (2021)
  10. Woolley, Thomas E.; Krause, Andrew L.; Gaffney, Eamonn A.: Bespoke Turing systems (2021)
  11. Gärtner, Janina; Reichel, Wolfgang: Soliton solutions for the Lugiato-Lefever equation by analytical and numerical continuation methods (2020)
  12. Hao, Wenrui; Xue, Chuan: Spatial pattern formation in reaction-diffusion models: a computational approach (2020)
  13. Kreusser, L. M.; McLachlan, R. I.; Offen, C.: Detection of high codimensional bifurcations in variational PDEs (2020)
  14. Kuehn, Christian; Soresina, Cinzia: Numerical continuation for a fast-reaction system and its cross-diffusion limit (2020)
  15. Lappicy, Phillipo: A symmetry property for fully nonlinear elliptic equations on the sphere (2020)
  16. Ly, Phong-Minh Timmy; Mitas, Kevin David Joachim; Thiele, Uwe; Gurevich, Svetlana V.: Two-dimensional patterns in dip coating -- first steps on the continuation path (2020)
  17. Marasco, A.; Giannino, F.; Iuorio, A.: Modelling competitive interactions and plant-soil feedback in vegetation dynamics (2020)
  18. McLachlan, Robert I.; Offen, Christian: Preservation of bifurcations of Hamiltonian boundary value problems under discretisation (2020)
  19. Siemer, L.; Ovsyannikov, I.; Rademacher, J. D. M.: Inhomogeneous domain walls in spintronic nanowires (2020)
  20. Siero, Eric: Resolving soil and surface water flux as drivers of pattern formation in Turing models of dryland vegetation: a unified approach (2020)

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