The Julia Community is simply amazing. Along the way I had my share of genuine but sometimes stupid and irritating doubts, everybody was really helpful. Slack is very active and very well organised. I’m really grateful to be a part of this community.

I spent the first last week of May going through literature on S-ROCK methods which I proposed to implement during my GSoC. After the first week I tried fixing bugs and getting the benchmarks for ROCK methods ready. I worked towards optimising memory usage in ROCK-methods, RKC, IRKC, and SERK-methods. Also we put in place certain step size limits to prevent the solver from going unstable. Also During this period I implemented SERK2 and ESERK4 which are similar SERK methods that I proposed but have ordrs 2 and 4 replectively.

With this IRKC and SERK-methods are almost complete and only their benchmarking remains.

List of Contributions

Performance for the above Stabilized Methods

1. Non-Stiff Problems

   • Fitzhugh-Nagumo
   • Lotka-Volterra
   • Linear 100x100
   • Rigid Body

2. Stiff Problems

   • Orego
   • Hires
   • Filament
   • Comparing Stabilized Methods for Filament with TRBDF2

Future Work

Going forward after discussing with my mentor I’ve decided to postpone benchmarking of SERK-methods to prioritize implementation of SROCK-methods. I plan to implement some basic stochastic solvers in StochasticDiffEq.jl, and then start with SROCK methods as detailed in my proposal.

All the problems for benchmarking purposes are taken from DiffEqBenchmarks.jl