Third Evaluation Report
With the addition of KomBurSROCK2 and SROCKC2 all the methods mentioned in StochasticDiffEq.jl Issue #73 are complete. KomBurSROCK2 is similar to SROCK2 for Stratonovich Problems.
| Solver | Description |
|---|---|
| KomBurSROCK2 | This is an explicit strong order 1 and weak order 2 solver for stiff Stratonovich type problems. This method is similar to SROCK2 for Stratonovich Problems. It is compatible with 1-D, Diagonal, Commutative, and General Noise cases. |
| SROCKC2 | This is an explicit strong order 1 solver for stiff Ito type problems. It has convergence of strong order 1 for 1-Dimensional, Diagonal and Commutative Noise. |
With this in place, I refactored the SROCK methods I implemented to only use vector type calculation. Further adding Tracked Array compatibility and fixing some bugs in general noise case in SROCKEM. Along with these I added Diagonal noise compatibility in 3-stage Split-step Milstein Methods and fixed bugs in error calculation in RKMilCommute when using adaptive setting.
Approximating Iterated Integrals
Now StochasticDiffEq has functionality for estimating Double Stochastic Integrals using iterative techniques as used in SDELAB with accuracy of order 1. These are required to get order 1 convergence in Milstein Methods for general noise case. The original paper was by Wiktorsson that is Joint Characteristic Function and Simultaneous Simulation of Iterated Itô Integrals for Multiple Independent Brownian Motions. Apart from this we use take advantage of Diagonal and Commutative noise cases to approximate these using less computational effort.
Apart from this I also made contirbutions to OrdinaryDiffEq.jl and DiffEqDevTools.jl where I fixed bugs in ROCK Method in case of negative dt, and fix noise type when noise is non-diagonal in analyticless_test_convergence. I also refactered SERK methods adding step-size limits to ESERK4.
List of Contributions during Weeks 9 - 13
StochasticDiffEq.jl
| Description | Pull Requests | Current Status |
|---|---|---|
| Diagonal Noise Case Three Stage Split-step Milstein Methods | #184 | Merged |
| Implemented KomBurSROCK2 | #186 | Merged |
| Vector Format for SROCK Methods | #192 | Merged |
| Implemented SROCKC2 | #204 | Merged |
| Implemented Iterated Integrals | #209 | Merged |
| Fix Error Calculation RKMilCommute | #218 | Merged |
| SROCKEM General Noise Bug Fix | #227 | Merged |
| SROCK Methods Tracked Arrays Compatibility | #228 | Open |
OrdinaryDiffEq.jl
| Description | Pull Requests | Current Status |
|---|---|---|
| SERK Cleanup | #808 | Merged |
| Bug Fix ROCK Methods | #848 | Merged |
DiffEqDevTools.jl
| Description | Pull Requests | Current Status |
|---|---|---|
| Fix Noise Type in Analyticless Convergence Test | #46 | Merged |
Future Work
With iterated_integrals.jl in place, I want to add Milstein Methods that take advantage of this to get strong order 1 convergence in case of general noise. Also, I want to add Benchmarks to show the performance of these solvers to the community and I SROCK method KomBurSROCK1 which has strong order 1 convergence using iterated_integrals.jl.