Last updated September, 2022.

Software projects

On this page you can find links to the source codes, developed by my students, collaborators and myself. Some of this material will eventually be moved or copied to Mercurial repositories, journal repositories and the Software section of DSWeb. Links will remain available here.

• Dynamical analysis of Liley's mean-field model
  Developers: Kevin Green and Lennaert van Veen
  Related publications: GV.
  Key words: mean-field model, nonlinear PDE, simulation, bifurcation analysis, finite differences, domain decomposition.
  Abstract: This package includes a code for the simulation and bifurcation analysis of the discretized Liley model on a rectangular grid with periodic boundry conditions using PETSc. It provides functions for computation of the vector field and the Jacobian, for setting up the grid and domain decomposition and for intializing the systems and handling data input/output. We will be adding data sets, initial conditions and other snippets necessary for reproducing our results.
  Download page: Source code and instructions are here.
• A parallel method for pseudo-arclength continuation
  Collaborators: Dhavide Aruliah and Alex Dubitski.
  Related publications: AVD.
  Key words: parallel computing, arclength continuation, scientific computing.
  Abstract: We worked out a way to parallelize the inherently serial process of arclength continuation, following an elegant, recursive approach. Hopefully, this work will result in a software package that can be applied to dynamical systems-type problems as well as implicit time integration.
  Download page: Source code and instructions are here.
• Green's function based time stepping for the KS IBVP
  Related publications: V4.
  Key words: initial boundary value problems, semilinear PDEs, time-stepping.
  Abstract: This is a Matlab implementation of a time-stepper for the Kuramoto-Sivashinsky equation with fixed boundary conditions that avoids numerical differentiation and linear solving. It serves as a demonstration only, the real power of the method lies in dealing with very fine grids and small values of the viscosity.
  Download page: Source code and instructions are here.
• Automatic detection of SNTC points with MatCont
  Related publications: VH.
  Key words: saddle-node-transcritical bifurcation, test function, MatCont.
  Abstract: Dynamical systems with codimension one transcritical birucations are common but not generic. In such systems, codimension two saddle-node-transcritical interactions can give rise to rich dynamics. With some small changes to the MatCont code, we can use a new test function to detect and correctly classify such interactions.
  Download page: Source code and instructions are here.