## Codes

Contact me for the following programs. Alternatively, you may look at public repositories on my bitbucket or github accounts.

• ### PseudoArcLengthContinuation.jl

Pseudo Arclength Continuation code in Julia. Allows for continuation and bifurcation analysis in large dimensions, possibly on GPUs.

• ### PiecewiseDeterministicMarkovProcesses.jl

Simulation of PDMPs in Julia based on this paper with speed on par with C. PDMP means piecewise deterministic Markov process.

• ### LSODA

A Julia wrapper to call the LSODA algorithm by Linda Petzold and Alan Hindmarsh. It solves ODE by switching automatically between stiff and non-stiff methods.

• ### Pytrilinos

I have been working with Bill Spotz from the Sandia Labs to develop PyTrilinos, e.g. the nonlinear / numerical continuation part, in Trilinos > v.12.

• ### Neural fields equations in PETSc

Simulation of Neural Fields equations using petsc4py. This allows parallel and fast simulations of models $$\frac{d}{dt}V(x,t) = -V(x,t) + \int_\Omega J(x,y)S(V(y,t))dy,\ y\in\mathbb R^2$$

together with the numerical bifurcation analysis. The number of unknowns can be >$10^6$.

• ### Hopf curves for DDE

Computing Hopf bifurcation curves for delay differential equations (paper), basically finding $\lambda\in i\mathbb R$ such that there is a solution in $U$ to

$$\left(\lambda+l\right) U_i(x)=\sum\limits_{j=1}^p\int\limits_\Omega J_{ij}(x,y)e^{-\lambda\tau(x,y)}U_j(y)dy,\ 1\leq i\leq p,\ x,y\in\mathbb R^d$$

or